Hmm... Actually, the "ninja mask" that many snow boarders use would be very cool. Get the "Winter Soldier" look going... I like it. :-)
Ummm, it's called a gaiter, and it's very useful for keeping cold wind and snow out of your face and neck area of your jacket....
And I wouldn't, they're deigned to keep that area warm, and will be pretty uncomfortable unless it's cold out.