All replies that say it is best to not feed it are completely correct.
That said, however, you asked a specific question, is a little bit okay? The answer is always qualified. But, yes, horses can eat some moldy hay without harm.
What causes the harm is a combination of several things, not all of which relate directly to the hay. Horses have a very sensitive gut; however, it is not typically the gut that is at risk. It is the lungs. Someone answered that moldy hay causes respiratory problems, and they are right. It is the inhalation of the mold spores that causes problems in the lungs. The symptom you will see is a hoarse coughing or wheezing.
But that's only part of the story. Horses that are kept in stalls and barns are at the greatest risk, while those that are free pasturing are at the lowest risk. The reason is that the stalled horses are kept in conditions where there is constant barrage of dust, and they never get the chance to clear their lungs. The mold spores can be the card that tipped the stack. But horses that are free pastured can go to a big round bale, eat some hay that has some mold in it, then get away from it and clear their lungs. We have had horses that inhaled enough mold to get the cough, but within a few hours or a day or two, they cleared right up.
So, while I would make every attempt to locate the worst part and extract and discard it, you can, in a critical need situation, go ahead and let the horse eat some of the affected hay, especially if they are kept out doors.
Typically "black spots" to me would mean badly deteriorated, rotted spots, which were caused by excessive contact with water to the point that the grass literally rotted. This is beyond mold, and should never be fed. However, if a horse encounters it, they will generally drop it from their mouths, and it doesn't pose much a risk to either gut or lungs. But, that kind of bad hay is usually easier to locate and discard than the more insidious internal mold, which is harder to see, has tiny white specks instead of black spots, looks like dust when you open the bale and the pores get blown about, and smells musty. That kind is harder to get all cleared out of a bale, and is the type that causes the lungs more problems.