In this area it's very very hard to get round bales that are horse quality. Farmers are very good at baling the hay just a little bit tough, & when it gets packed into those round bales it just doesn't keep. We've tried round bales different times & so often have ended up with mold, so end up having to burn the bales. This year we've been feeding round bales that I got from a neighbor. He baled them in perfect shape--no mold whatsoever in any of them, some are grass, some grass/alfalfa & some 2nd cut alfalfa. The 2nd cut is dusty--not a moldy dust, just a dry leaf dust as the hay was actually baled a bit too dry. When you tear it apart the leaves all fall off the stems.
We always fork our hay out to the horses, we don't set bales out for them--in the first place, we have no tractor to move bales with, & in the second place I don't like them sticking their heads in the round bales. Even if the hay is good, with no mold, some horses do end up with dust allergies, even heaves, just from eating the round bales. It's surprising how much dust there is even in the good bales.