Horses do sometimes react to feed - it can be hard to tell if it's an allergy or some other kind of sensitivity (just like in humans). We have no clue how many actually have food allergies, as skin tests don't work well on horses. The only thing you can do is an elimination diet - and what if the food is something in the pasture? Oh, and antihistamines don't work well in horses either.
So, yes they can, and it's a nightmare when they do.