Some plastic parts used in bikes become brittle at around -30 to -35 C. If you bump them on something then, they might break. This is the highest temperature at which anything permanent can happen to your bike because of the cold. Freehubs can act up when it's at all below freezing, but that's not permanent damage: they'll be ok immediately when they heat up. And you can combat that with proper grease.
As for metal parts, I have no clue. I suspect that the level of cold which will permanently damage metal is not something in which a human will survive.