I'm apparently not one of the super-manly-men that have posted previously. Because even in what is the very mild winters of Southern California, I still keep one of those "buffs" rolled up in my saddlebag on especially cold days. Frankly, a 2-hour long continuous blast of 30º air in the mouth is just unpleasant. And while it might have to get down to absurdly low temps (something like -19ºF) before frostbite is a risk, having the tip of my nose feel like it's going to fall off is a sensation I can live without.
I just use one of these:
12-in-1 headband because it's cheap, and it works. Keeps my nose and lips wonderfully unfrozen.