Stacking loose hay is a lot of hard work. Piling the hay on the wagon was fun if you were young and on top placing the hay but not so much if you were on the ground forking it up, esp once the load was half full or better.
We used to store loose hay in the barn..we had what they called a hay fork which would run out on a track until it was over the wagon and then drop down and bite into the hay. It saved an immense amount of work. Ours was a little different than this one
http://www.redpowermagazine.com/forums/index.php?showtopic=60423 but the principle was the same..we used a tractor but it apparently can also work with a horse or mule.
If being stored outside I would strongly suggest piling hay on pallets to keep it off the ground and use the tarps to cover them with.. I have found that with the big round bales ground moisture causes as much hay loss in uncovered bales than the usual rain, and more than in covered bales. With small bales or loose hay, though, you need both - rain will wreck your uncovered hay in a hurry. I have stooked lots of small bales and don't see the point, a good rain will soak into them and spoil them almost as fast as if they are loose hay..better to use the time to put them under shelter instead, imo. It's so sad to see lovely hay all carefully stooked in a field slowly turning black, such a waste of time and effort (and money!)Unless of course the idea was to make
compost or mulch!
If loose hay isn't covered then the top has to be pretty carefully shaped so as to shed as much rain as possible before it simply sinks in. After going to the trouble of making good hay I wouldn't take the chance, personally, of leaving it uncovered. Years ago people didnt have other options.