I suggest wearing your jacket the other way around. In Norwegian you'd call it "back-front", what's that called in English? So the hoodie would cover your face. I know there's a word for it. Damnit, I was going to phrase that as a really short and precise comment but that didn't work out.
Is it backwards? What's really confusing is when you put it on backwards without realizing it. The whole world turns mysteriously dark and you think, "Oh god, I'm suddenly blind!" But at least your face is shielded from the wind. (Long, rambling comments are just as good as short ones!)