Thanks everyone, I will definitely use pallets. Would anyone recommend using a double layer of pallets, both for extra strength and extra ventilation? The barn does have a cement floor but I also like the idea of putting a moisture barrier down there just in case. When we go out there again, I'm going to check really carefully for signs of water entry, also, just to be sure that there isn't going to be any moisture. Actually, now that I am thinking about it, I think the barn has little covered channels that run down either side of the aisle. But I'm not sure where they drain to. I will check that out also, and make sure to not cover them with my hay.
I will also tell my husband no woodworking in the barn. There is another outbuilding already set up as a workshop (although for weaving, not for woodworking) that he can use.