Under what circumstances would you buy round bales of hay for your horses that have been stored outside? I know in a perfect world, they should be stored inside, but that is not always possible. So does the manner in which they store them matter? Stacked vs in rows? Is one better than the other? How about wrapping? Does net wrapping preserve more of the hay? Does net wrapping have to be removed before feeding ? What is the oldest hay that you would consider? Only hay from the current year or last year? How long could a round bale stay good being stored outside in the elements?
If it's just for 5 or fewer horses on partial turnout I wouldn't bother with rounds... the hay would go south before it was eaten. HOWEVER, the way a round bale is made will "thatch" the upper layer; rainwater sheds right off, and the outer funky-looking layer can be removed. The inside looks like the day it was baled, even after months under snow. Once the horses start eating the bale you lose that thatching effect, so it's best to feed the roundbale under cover or have enough horses that the bale won't exist anymore in a couple of days.
Plastic sheeting bale wrap is a pain in the rump to handle, but fairly easy to remove. Netting is harder to get off, IMO, especially if the bales are stored outside and snow fuses to the hay through the net. ABSOLUTELY remove whatever kind of wrap is on the bale, whether twine, net, or plastic sheeting. The guy we bought our farm from just dropped wrapped bales and left the plastic sheeting lie... yeah, we're still pulling sodded-in wrap out of the ground 10 years later. I've seen horses with rope burns around pasterns from catching up in looped twine and netting. Remove it and put it in the trash. Plastic sheeting can foster mold growth if the grass is still wet when it is baled (sometimes just turns to haylage even in an individual bale)... use with caution there, but the white plastic is more of a cow hay phenomenon, and they are a bit tougher digestively than horses.
Right now our local area is in a major hay shortage, we'd probably buy anything under 2 years old for our cows. For the horses, what we do buy was baled (square) within the last year. We do our own square bales, and it's rare to have any hang around longer than that. More often we buy an extra 50 squares to supplement them until we can cut again.
To my knowledge, stacking vs. rows doesn't matter.
A concern that I have is the horses eating the hay with their heads up, and dust and the like going down their noses (I don't use hayracks, either). I know a guy with 8 horses on full turnout all winter, and he will cut the wrap and unroll the hay like a carpet. The horses get the grazing effect, and the hay.