you should have spoken to me a week ago. I was out on foot - in the middle of that polar air mass that hit the Midwest. I was also unprepared, since I was just travelling through the region. I am mildly surprised that I didn't get some frostbite. The wind chill temp was -30 to -40 degrees that night.

As an emergency measure, get ANYTHING over your face to cut the wind. A large bandana would help. I started using an old T-shirt as a bandana ... I didn't cut it. I just wrapped it around my neck and face.

Otherwise as people have indicated, get a coat with a "tunnel hood". Use a couple of pegs or clips to close off the tunnel, if the wind is very strong. The only issue is that you can hardly see when you do that. But if your face is frozen, you can hardly see anyway.

good luck,
Pete