In order for condensation to occur, the amp must be colder than the ambient air. If the amp can be brought to room temperture before the warmer, moist air hits it, condensation won't occur. Once the amp is the same temp as the barn air, condensation shouldn't be an issue unless the air is quickly heated with something that also increases humidity (steam heat, a humidifier, etc.) Because the barn has little protection from the outside, condensation becomes an issue when a warmer, moister weather system moves in as condensation will occur on the colder surfaces in the amp. In this situation, covering the amp may help as long as the moist air doesn't touch the amp's internal surfaces. Keeping the amp a few degrees warmer than the outside air should minimize the condensation risk.
Either way, I don't know if I'd subject my amp to the risk, nor would I want to keep my amp in a sub-freezing environment. As others have said, condensation is not a good thing for amps.