In terms of comfort and warmth sure a thick soft wool hat or something like it is the best. But when you have to weigh safety concerns then the helmet takes on a more important role. Some people's insurance won't cover them while bike riding if they aren't wearing all the right safety equipment.

I go back to a helmet every winter, even after riding just hatted (which is how I ride in the summer). I do wear a wool cap underneath, but the helmet provides a wind barrier for my dome; when temps drop below 15F, the wind generated by cycling starts to hurt, even through wool. And winter crashes tend to be low speed, slide out affairs; which is exactly what bike and ski helmets are designed for. I've bounced my head off of the ice with and without a helmet, and I much prefer with.

Well, some time ago I either rode without any head cover or with a wool cap maybe below -12C (if I did not forget). However, after I collected my friend and pieces of his helmet after his flight over handlebars over a twig, next day I put on a helmet and never took one off except for short errands. Since then I flew over the handlebars myself at least once but already wearing a helmet. No, I did not anticipate flying. When riding in winter I put on a skiing helmet which, in fact, I trust more than a cycling helmet, as providing a more thorough coverage. I wear a helmet during skiing as well, after attempting to fully scalp myself on one occasion. Right now at times I feel uneasy when getting into a car and missing a helmet.

I use a ski helmet and I particularly like the ear covers. I start wearing the ski helmet and goggles in late November because the cold wind makes my ears hurt like crazy and I'll accept any excuse to wear goggles. So sad. So true. When the worst of the cold weather is over in early March, I'll wear my bmx helmet again, as well as the goggles. The bmx helmet does accommodate the goggles very well.

sixsixone
 

First if you are riding in snow, this is not the time to give up your helmet. All my spills have been in the winter and I am greatful for the brain bucket. I wear a SixSixOne helmet. It is great. It has great ventilation on top and in front and back which allows me to thread my head lamp through it. I am able to wear any type of hat underneath and as its made for BMX riding it offers great protection. I bought at my LBS for I think 25.00 and I am able to wear my ski goggles with it. I ride in snow regularly.
Mine is bright pink but they come in other colors but I like to be seen by those in the rolling coffins when I ride. Attachment 183343

During below-freezing weather, I wear Pro-Tec's MultiSport half-cut helmet. Yes it's certified for both snowboarding and bike use.

The Pro-Tec has a ski-goggle clip (see my attached photos), and it has more vents than a ski helmet, plus it has a removeable ear-liner and vent filters if you want more ventilation.

Been using this helmet with my Anon ski goggles for the past 3 winters, works perfectly for me.

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