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Biking in the Northeast has become a challenge lately because of the cold; my ears freeze.

I can't wear a hat (because of my helmet) - I never actually tried, maybe I can.

Sometimes I'll put my hood on and then my helmet on top of that, it looks really weird. (Helmets look weird, hooded helmets are a whole new level of weird.)

I'm wondering if there are any other solutions.

_{I normally have a single Bluetooth earbud in one of my ears as well, not sure if that makes a difference.}

When it's cold enough here, I use a toque (or beanie or knit cap or whatever you call it in your part of the world) under my helmet. It's thin enough that a small adjustment of my helmet is all that is needed for a comfortable fit. Mine fits over my ears and doesn't interfere with headphones.

Try searching for the term "ear band". They tend to be thin enough to comfortably wear under a helmet, and the good ones are fully wind-resistant, yet breathable.

If you have an open ventilation-style helmet, I recommend a helmet cover as well, which is a fabric sleeve that stretches over the top of the helmet which also significantly cuts wind passing through, and may be easier to use instead of a jacket hood (not to mention more streamlined). Install once per season.

Balaklavas or "dickies" are also good to protect the neck and shoulders, and there are also polar fleece neck warmers that may be more comfortable and can bunch up nicely under the back of the helmet.

Any quality of biking glasses/goggles are useful, too — look for ones with clear lenses — which will ensure your eyes don't get a full blast of cold directly.

There are many headwear items available that can keep your head and ears warm in cold weather, that are thin enough to fit under a helmet (and not look too strange).

Just google 'bicycle headwear cold' and you'll find many choices; from headbands that keep the ears warm, but allow for cooling from the head; simple skullcap type hats that insulate head and tops of ears; hats with extended ear and neck protection; and full-face and neck balaclavas.

Having a proper headwear under your helmet should be a preferred way to keep oneself warm. However, for the picture's completeness, I want to mention using different types of helmets in winter: full-face MTB and moped/motorcycle helmets.

They are heavier and pricier than regular "open" helmets, but they have much less ventilation, and often come with some sort of goggles to cover your face even more. Both aspects are beneficial in winter.

Another thing is that these helmets are also certified for riding two-wheeled (non-)motorized vehicles, if this is something you are concerned with. Other types of "warmer" helmets, such as ski helmets or water-rafting helmets, may not be tested against the types of impacts that may happen in a bicycle/motorcycle crash. You need to check certifications of a helmet before using it in possibly unintended conditions.

I have a thin material tube that can be used for a lot of things. Also called a headsock or necksock or a buff.

I wear mine around my neck, with the top edge at my mouth/nose, and up over my ears at the back. The lower edge rides on my shoulders and slightly over my collarbone. Some buffs have a split on both sides and cover the top of the chest a bit.

Then on top of this I wear a cycling cap with a visor (my commute is into the sun both ways and helmet lacks a visor.)

Downsides, covering the mouth leads to problems with dampness from the breath, and contributes to steamy glasses.

Also, if you're biking fast enough you warm up with the effort and can get too hot, even in the cold.