Exposed skin freezing at -32? (Celsius, I assume. Only about -25F..) Nah, not THAT fast. But playing the guitar would be tough and not good for the guitar.
-32*C with no wind isn't bad at all. In Manitoba it is also dry. It feels much different than -5*C ( +22*F or so) when damp, like out on the west coast. That humidity chills me to the bone.