Mwahahaha! I forgot to say that I found a nice winter hat this weekend. It’s basically a sort of woolly (acrylic) knitted beret or snood, except that… it has a visor brim like a fisherman’s cap!
I don’t actually think this would work for _deep_ winter, but for early and late winter, it should do fine. Also, it actually threatens to approach fashionability and cuteness, which are good for shock value when found on me.