Once hay is cured I am not sure how much if any good salting it will do; that's more something you'd do when putting it up green, as much so it doesn't heat up too much and burn the barn down as to prevent mold.
Pallets can be cut in half to fit into the back seat of any car. TYpically you will just be sawing through 2-3 2x4s to do this, not bad. Keep saw in car at all times
Best thing IME is to put a tarp down, then pallets over it, then your hay up on that, making sure NOT to stack the hay against the walls, especially not towards the bottom of the stack -- you want a foot or more of space there to encourage air movement. Not a huge deal in a vast hay mow but in a small storeage space it is VERY worthwhile, even though yes it does marginally decrease the amount of hay you can store there.
And yes, as everyone says, don't feed moldy hay to horses unless the alternative is starvation. Soaking/rinsing reduces respiratory problems but does not change the possibility of colic one iota.
If you compost the moldy hay for a few years (just pile it somewhere out of the way, in a flat-topped stack, and ignore it) it will make EXCELLENT mulch, and a year or two after that it will become EXCELLENT soil amendment to improve your garden
Sorry you had to learn this the hard way, at least it's not the *most* expensive hay year ever in which to learn it
Better luck next time,
Pat