If it's more hay than they can eat in a week, I would put it under some kind of cover.
Nutritional quality does degrade with exposure to sun and rain, etc.
Depending on the type and condition of your horses, you may find that you need to restrict their access to it to keep them from getting too much.
Normally there's no such thing as too much forage, but I have a piggy little QH who's the equine equivelent of an air fern; when I put out a round bale I either have to shut him off of it on alternate days or make him wear a grazing muzzle. The round bales I feed are pretty good quality, but even with lower quality hay, if you have a piglet, you may want to restrict access so they don't get a hay belly.