Horses are huge animals and often have to be put down for injuries to their legs. It's a shame to let meat go to waste. I don't know about killing horses in their prime though if that's what they do.
This in part was why the horse meat scandle was such a problem in the UK.
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.