Not an elecrical issue. Most fixtures are designed to be mounted at only two points so as long as those fall over something solid to screw into, it should be OK.

The only real issue with unheated spaces is that some fluorescents don't do well when it's sufficiently cold.

Thanks Ron.

A good, modern electronic ballast will strike down to 0 F if you don't mess with low-output lamps. If you want to go lower than that, you need low temp ballasts and I bet they are pricy.