All of my honey supers stay here in NY for the Winter, stacked on wearhouse pallets w/ a plastic tarp cover and a pallet on top to weigh the tarp down so the top supers don't blow off. I have never had any wax moth damage in those stacks.
Deep supers used for brood supers will have some pollen in them. If they don't get back on strong colonies early enough in the Spring they will often have wax moth damage.
Seems like the presence of pollen is the problem.