If you are facing anything less than Siberian weather a tube amp should handle the cold decently, although the bulbs are made of glass which might contract to the point of breaking at arctic temperatures. However, there is a far more pressing issue to worry about, in that the amp must always be warmed up before use if it’s been previously stored in a cold environment.
So always wait for something like half an hour before a gig for the amp to reach room temperature before turning it on. Really, this is advisable with most pieces of electronics.