A generous layer of bear grease slathered over your face will help keep the cold out. How thick to make it? Use the Phil test. If Phil looks at you and he doesn't say: "Oh my god, what's happened to your face?!", then it's not thick enough.
If you can't find bear grease, bacon drippins will work almost as well.
The question is whether letting the cold in or covering your face with bear grease builds more character. Though I haven't tried the latter, I'm inclined to think that it would be a strong contender in any HTFU competition. Which is really why we do this stuff, right?