Keep in mind too, that by-products in horse feed is not the same as by-products in dog food :)
That said, I don't know any off of the top of my head other than oats, but I do know that it is definitely better to feed on a consistent basis and not on an occasional one.
Then again, if he is an easy keeper and does not get that much when you get him (more like a treat sized portion), I don't think it would matter much. (IMO)
Horses don't need tons of protein...I'd shoot for something middle of the road.
ETA: Most horses dont need tons of protein...there are some that do, but most dont :)