forcing many mammal species to become cannibals causes disease, and that was what was causing the mad cow, feeding cattle ground up members of their own species. It was common for a long time.Apparently some were getting meat and bone meal and that was one way "mad cow disease" was spread. It was never standard practice and many places legislated against it when it came to light.
interestingly their is a human equivalent, which has been documented in several circumstances.
I don't think a horse is made to be an omnivore exactly, but the odd bit of animal protein wont kill them. Pickles will steal cheese burgers any chance she gets.