[HeyLaughingBoy]

That won't happen.

If the horse has to be euthanized, unless it happens far from vet care (say on a distant trail ride), it's going to be given a lethal dose of sedative. If it does happen far from care, then it'll be most likely shot in the head and the carcass burned or left for predators if it's not possible to dig a pit for it.

Source: live on a horse farm and have had to deal with weak or dead horses.