There are thin hats that I wear under my ski helmet that are a type of fleece(?), they work well under my helmet and keep my bald head warm at the same time. They also have them in full face masks like guys wear snowmobiling, sure the guys in Minnesota could tell you what they are called. I've always called the smaller ones I've worn a toque(spelling). They are very thin, but they breath well(I sweat a lot) and they block the wind. If you helmet won't stay on well when you look up because of your hat its not giving you as much protection as it could be, kinda like what Fauci said about masks
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