Well it's not as if we have to don ski masks or anything too drastic. It's snowing, not blizzard...ing. Hats are something that both shows face and keeps you more or less warm. Or you could go headgear-less.

Granted my character is mostly going to be wearing a mask/helmet whether we're in winter or not, meaning the whole weather problem doesn't really apply to me, so take what I say with a grain of salt.