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Use a pencil. They do not freeze and can be easily sharpened. You might also use a grease pencil; they can write on metal, plastic, wet, oily, or waxy surfaces as well. These don't always afford the finest points, so if this is a concern, consider a fine-tipped sharpie, but, Sharpies are still susceptible to cold and wet weather.

EDIT:
Now that you've edited your question, I can offer a little more advice.

• Use a wearable video camera, like what cops use, or a mounted Go-Pro kind of thing. Then survey your inventory and review the video clip later when it is warm. This might mean twice the time, which can be expensive for you (time is money...) but you might delegate the video review to someone else. The nice thing about this is you might catch something you might not have seen IRL. Also, it can provide proof for auditing purposes, depending on the reason for the inventory review (eg, are you looking for signs of damage from weather or animals; or maybe you're looking for vandalism, disease, or theft? Are you providing proof for purposes of sale, auction, insurance, or property value?)


• Use gloves with cut-off fingers, so only the finger tips are exposed. Wear a jacket with deep pockets, and in those pockets, keep hand warmers. You can use refillable Zippo ones that you can get from the camping section at Walmart or Target; or you can use the disposable ones you can get also from Walmart and Target, or at most chain pharmacies. With these gloves and hand warmers, you can use any writing implement - pencils, markers, sharpies, smartphones/tablets, etc.

EDIT2:

• You've got a lot to survey, a drone with video capability might be helpful.

I have previously used a tape recorder and nowadays, a smartphone or tiny handheld microphone. Then I simply speak my observations and findings in a way I know I will be able to easily tabulate when I am inside once again.

If it is too windy to use an outer microphone, usually putting it below clothing layers will do fine. If it's muffled, I later boost the audio in Audacity -- it doesn't need to be production-quality.

This is also useful when it is too windy to write on paper, or too snowy + windy to see what you are writing.

To address the issues you're having with audio-based solutions, keep the phone inside your clothing and use a "hands-free" headset (wired). This will stop the phone dying due to a cold battery, which incidentally I've never had trouble with on a range of Android phones. With the right software you should be able to record when the microphone button on the headset is pressed (but I don't know of anythign for iPhones as I've never had one.)

If you do use the phone, I suggest you keep an audio file and pass it through dictation software later, then you can refer to the audio file if there's confusion.

However a fat pencil and the minimum gloves you can get away with are pobably a more robust solution. Flip mitts over those gloves will allow you to warm back up again when you've got a longer break, but the inner gloves should be selected to be sufficient for reasonably long periods; in partiocular they should be windproof.

One thing that hasn't been mentioned so far is the need to have a workflow such that your writing (i) is minimised, and (ii) can be big. So tick-boxes or boxes for numbers where possible -- that should get you a long way in your inventory case. A customised notebook with laser-printed (not inkjet in case of damp) pages is helpful in many situations.

When I was hunting, I found that the best way to keep my fingers warm, while still allowing me to free them for delicate manipulation (loading a magazine, etc) was to wear "convertible gloves" - that is, fingerless gloves with a mitten pouch that could be slipped over your fingers when not writing. Additionally, adding a chemical hand-warmer to the mitten section makes warming your fingers back up relatively quick. You'll have to shop around for a pair that is quick to convert to finger-less and back to mitten, so you can cover up between turns.

The other option is to keep your pen and clipboard on a lanyard so you can pocket your hands with handwarmers between notes.

When I worked at a salebarn in the winter we had this problem and the solution was multiple pens inside your shirt pocket under your coat.

Pens will work for a while then get too cold at which point you switch it out for a new warm one.

You might also look into the mittens that have gloved fingers inside, you can pull just the top off to write while most of your fingers (all except the tips) are still covered.

Prepare a form for the information you collect.

Make the blanks big. Fill in the form by grasping your "pencil" in your gloved fist. Use an over-sized writing utensil (so your fist doesn't cramp). Revert to bare fingers when necessary.

Blanks for numbers are easy. So are checkboxes. If there is text you need to write, try to create options ahead of time so you can just enter A, B, C, etc.

You might "waste"/use more paper, but that cost will be offset by the man-hours saved.

One time, during a winter research project, it was only after after a full-day ski to the study site that we realized that none of us had a pen or pencil. So we wrote the numbers in the snow with a twig and took a picture.

I realize this doesn't directly answer your question, but it made for an entertaining story.

-10C (14F) is not that cold.

If you keep moving a thin "glove liner" or "running glove" should be warm enough for a while. The glove liners are thin enough where a regular #2 pencil will do fine. Then put on a pair of "Over Mitts" over the liners when you don't need to write.

You're using a waterproof field notes book, right?

You're using dot tally to reduce how much you have to write?

Society of American Foresters has a forum on their website for Inventory questions. Maybe ask in there? https://www.eforester.org/Main/Community/Join_a_Working_Group/Main/About/Working_Groups.aspx

There are some pens that are made for extreme conditions such as the uni-ball PowerTank Retractable Ballpoint pen. I've never personally used one of these but it has many positive reviews on Amazon. There is also a freezer test performed on this pen with the following results:

Source: OfficeSupplyGeek

Most answers seem to assume the writing implement is the problem, but the asker specifically states that his comfort is the problem. I can think of two solutions.

If possible, figure out how to simplify your inventory. Consider writing in ways that don't require a large amount of dexterity -- I would consider tally marks.

If you need more detailed notes, consider how you can heat your hands with thinner gloves. You could do fingerless heated gloves, or shove a handwarmer in the palm of the glove.

Pencils. Pencils are also approved by the Bundesmarine (German Navy).

I remember how pencils just worked when we stood outside in the rain and in the snow at temperatures around 0°C, and us recruits practicing morse codes. Unfortunately I have no other quotation for this, except myself (Signalbetriebsdienst class of Winter/2004 at Bremerhaven).

Paper was the bigger problem. Once wrote down, the notes stood there. But it wasn't really easy to not rip the wet paper apart while writing. It's best if you're equipped with both hard and soft ones. Use the soft ones within bad conditions and when the paper is wet.

Baustifte/Zimmermannbleistifte/Carpenter's Pencils are usually in the HB range, though they have a big diameter core. If you want to draw on stone or other materials, use one of these, or a standard pencil with very soft core (2B or softer).

Also, especially when you sport soft pencils, it's a good idea to have multiple of them ready to use, such that you don't have to sharpen them when you can't afford it.

I write software for a company that supplies an application for field engineers to use to collect field data with a hardened android tablet. I expect you could use a text editor in a hardened android tablet to take notes. The value of this is that the notes can then be exported to a desktop (our software transmits it to a cloud server) and you won't have to worry about transcription errors, losing the paper, or having the paper become unreadable. There are gloves with wire embedded in the fingers to allow you to work on touch screens with them on. Or you could look for a tablet with a stylus, though a stylus typically needs electrical contact with the skin (mentioned as the gloves may have a broad contact area. But a stylus can be used with gloves like that). Sure it is a lot more expensive than paper and pen but the cost of losing a piece of paper and having to do the work over is high also and you only have to enter the data once. Paper leads to transcription errors, values in wrong fields, etc. Not saying you should look for something like we produce but you might look into a .pdf form you can fill in and then store and print.

Depending on the complexity of the notes, you may not have to sightwrite them. So, wear a warm but roomy coat, pull in your arms, and take your paper and pencil notes that way.

Think of the basic triangle - you need warmth, dryness, and wind-free.

OP's question does not mention being wet but does reference the cold AND the windchill. So limit the wind with some kind of windproof shield. Here's a generic "outdoor clipboard".

So the plastic lid keeps rain off, but will also act as a wind shield.

It will not really act to hold warmth though because of the large opening

I would suggest a pair of good waterproof winter gloves instead of mittens. These will keep your hands warm and protected from wind and still allow for enough dexterity for writing with a pencil.

Your question made me wonder how Robert Falcon Scott wrote his final diary entries on his trip to the South Pole in 1912.

This article, from The Guardian, Scott of the Antartic's final diary published online says with certainty that Scott's diary entries on the journey to the South Pole were written in pencil.

Readers can, from today, pore over the pages of faded pencil
handwriting that make up one of the most famous diaries in the world –
Captain Robert Scott's journal of the final months, days and hours of
his doomed 1911-1912 expedition to the South Pole.

The British Library has launched an online facsimile of the complete
last diary alongside extensive extracts from the two earlier volumes. (emphasis added)

History Channel on Foxtel describes Scott's final entry:

On 29 March 1912, in a weary pencil script, Scott wrote the final
entry in his diary: “Last entry. It seems a pity, but I do not think I
can write more–R. Scott–For God’s sake look after our people.”
(emphasis added)

The interior of Scott's tent was undoubtedly below zero C. This was Antarctica in March, and one of the colder Marches. Nature News, in its article Scott's Icy Death says:

the last entry in Edward Wilson's diary is a poignant: "Turned in at
-37° [F]" [-38 C].

Wilson and Scott, with Bowers, were in the same tent. Wilson's final entry was a day or so before Scott's.

Another source from the British Library mentions Scott picking up a pen, but the reference to a pen was probably a literary expression, not a factual description of what Scott used.

Fisher Space Pen. Writes down to -30F and won't leak no matter what (say, from altitude changes going up a mountain.)

https://www.spacepen.com/about-us.aspx

(And I have no connection to them other than being a satisfied user. At a desk I consider gel ink pens to be superior, but nothing beats a space pen for reliability--if I'm carrying a pen it's a space pen.)

Approach: Audio recorder with speech-to-text software

Issues:

• Audio recorder must work at freezing-cold temperatures


• Recordings must be processed afterwards by speech-to-text software


• Transcribed notes must be reviewed

Let me suggest that some acclimatization may help (though I'm not sure how practical this is).

• I was personally rather astonished how much we can actually adapt to cold weather: I spent a winter in Winnipeg (office job, no outdoors job). Nevertheless, whereas I had been freezing on the bike in windproof + light fleece pants/jacket in November in +5°C rain, in March when it got warm to "only single digit negative temps (°C)", I was biking in just summer outdoor pants/T-shirt + fleece, no gloves, no cap/scarf and feeling very comfortable.




• First conclusion: fall/early winter is going to be the most miserable time in the year because you're not yet accustomed to the low temps - still it is probably impossible to do this in any other season.



• 
  

  According to Hanna Kaciuba-Uscilko and John E. Greenleaf: Acclimatization to Cold in Humans, NASA Technical Memorandum 101011, p 18, local cold adaptation (hands) is possible as well:

  
  
  

  
  

  It was proved that people who habitually expose their hands to cold-for example,
  Eskimos (Miller and Irving, 1962), Arctic Indians (Elsner, Nelms, and Irving, 1960), fishermen (LeBlanc, 1975; Krog et al., 1960), workers who fillet fish (Nelms and Soper, 1962), and lumbermen (LeBlanc et al., 1976)- respond to local cooling of the hands with much less pronounced cutaneous vasoconstriction, and with more rapid onset of vasodilation than occurs in unacclimatized men. Thus, they tolerate cold-stress better than men unadapted to cold.

  
  

  
  
  

  So it may be possible for you to prepare for that inventory by deliberately exposing your hands to cold beforehand.
  (Biking, I find that it takes my hands, ears and nose get cold for about 3 days to a week with the first frosts in fall until they "remember" how to heat themselves at those temps. But then, I find cold adaptation much easier than heat adaptation. And my impression are that people are very much not the same in that respect.)

  
  



• Whether it is worth while obviously is for you to decide. However, you may also want to take into account that it may not be "only" a question of being uncomfortable but that working in cold environment is associated e.g. with increased incidence of rheumatoid arthritis.




• Obviously, keeping your fingers warm is only possible if your body core is warm. You could try whether warmer parka/long johns helps as well (parka is probably easier to get on/off). Also, there's a rumor that not only overall food status but protein in particular is important for non-shivering thermogenesis.

Thoughts about gear:

• From your post, you're able to do things in not-too-thick gloves, so maybe 1+1+3 shooting gloves would be a consideration?




• I'd probably try to have as much pre-printed as possible.




• As kids we used to have mittens with a line (so they wouldn't get lost when taken/falling off).
  A similar line with a very roomy mitten may allow you just put your hand in and out of the mitten without hassle. You you have to expose the fingers only for writing down your Mountain ash line, but they're in the warm while counting the pots.
  
  This line of thought directly leads to the invention of the muff. A "traditional" one for warming your writing hand while not writing, or maybe you could make a more specialized one yourself that accomodates your hand and just has the pencil sticking out, so you can keep it on while writing.
  
  In addition, a traditional muff has space for a heating pad.

Use Noodlers Polar Ink. It is specifically designed to work down to very low temperatures and has been tested in Antarctica.

https://blog.gouletpens.com/2017/01/noodlers-polar-ink-goes-to-antartica

The inks are also "bulletproof", that means they are very permanent and don't fade or wash out.