What about a storage bin/facility? May not be heated but its out of the weather, shouldn't cost too much for a basic unit. Monthly rent may suck, but its cheaper than paint repair (moisture damage, tarps doing damage, etc, etc.)

Looking at topside's post, I would have to say it depends on how well the place was built. Is there ventilation? The only time I had moisture problem here along the swampy Gulf Coast was when I rented a bin made out of corrugated tin with a dirt floor.