I purchased 2, 12x20' portable garages from a local hardware store ( on sale for a out $250 each) Basically they are a metal frame with a heavy duty fitted tarp over the top and have a roll up door on the front. Inside, I laid a tarp directly on the ground and then laid a layer of pallets on top of that. The hay is stacked on top of the pallets so that there is a out 4-6" of air space between the tarp and the bales. We stacked to the roof, but made sure to allow a bit of space on the top and sides for good air circulation. Last winter I got 220 bales in one shed and never lost even one bale to mould, wet or rot. I still have a out 8 bales left over from last October that are perfect. The covers are still in great condition, so we have done the same this year. I just got 360 bales and stacked them in the two shelters. To make sure everything was dry, I kept the front flap open for a couple of hot days to ensure no condensation on the inside, and we made absolutely sure the hay was nice and dry when we got it.
Summers here can be very rainy, with rain showers almost every day. I check regularly to ensure the shelters don't sweat from the humidity, but so far, I have had none, so the air flow is good. Once winter comes, it will be frozen here for a out 6-7 months, so I don't need to worry about moisture. It is also much easier unzipping the flap and grabbing a few bales than fighting with an ungainly tarp. The snow slides right off the top.