I grew up in rural North Dakota, here's what happens. You walk outside and inhale, and your boogers will immediately freeze in your nose. It feels.... odd, I've no way to explain it properly, it honestly is something one has to experience. The general rule is below about -10C or thereabout you blow your nose before going outside. That or you're going to wait for it to thaw and then blowing your nose.

Doesn't have anything to do with frostbite that I'm aware of.

When its that cold for shits I would take a full cup of boiling/hot water and throw it in the air. Making snow is fun.