I am assuming the plan is to drop them in the field. No cover.
I don't see any structures in any of the fields around here for covering round bales...
Most horses, even most little piggies, are smart enough not to eat moldy hay, unless they are literally starving. There are a few who will, but I used to board at a place that plunked down round bales and no one ever had a problem. You should be fine.
Square bales have me curious. Some local farmers have gorgeous 2nd cutting/alfalfa in these huge square bales...
Almost all the hay ranchers here in NV are baling in the "big" bales (3' x 4' x 8'.....weigh about 1250 on average) for a number of reasons....they are desired by the dairies and that is where much of the hay raised here goes....and they are impossible to steal from a stack if your stack isn't at your house and under watch. No one drives up in a station wagon and steals one...not even in a pickup!!
As a result I've fed the big bales for several years. They are put up in flakes just like smaller bales but each flake is equal to about 6-8 flakes off of the "small" bales (125 lbs each) depending on thickness. I just pull a flake down and use the pitchfork to break it into 6 nearly equal pieces and feed them. I have to drag hay to the other half of my place (across the road...can't store hay there as the mustangs get to it!) so have a sheet of heavy steel about 6 x 8 and pull it up to the bale, drop enough flakes to feed all the horses over on that side and just drag it across the road.
The only problem I've had with big bales is if one is rain damaged you loose a lot more hay than if one small bale is damaged. My hay guy delivers them to me and drops them where I want so that's cool...the small bales I can get I have to haul myself as the harrow bed that hauls them is too big to go through the underpass under the freeway and isn't allowed on the freeway so he can't get to me with it.