We never feed any hay that has mouldy or rotten sections in the bale. Your horses may pick around the bad hay, but don't forget that their heads are buried in those bales, and they are ingesting/breathing the mold spores. While it's true that mould is everywhere, and is somewhat unavoidable in smaller amounts, by feeding round bales that have visibly mouldy spots, you are asking for trouble.
We put up our own rounds and squares, always stored on pallets, always under cover right away. I will not take a chance with their health like that.