They do exist, and you see them on working horses to prevent the horses from pooping on the roads. It's not so much of a diaper, though, and more of a burlap s

They do exist, and you see them on working horses to prevent the horses from pooping on the roads. It's not so much of a diaper, though, and more of a burlap sack that's suspended like a hammock underneath the "business end" as it were. Note that this only works for poop; I haven't seen any solution for the voluminous amount of pee a horse can produce.