That Japan allows boats to roam to far waters without punishment is very different.
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.
This in part was why the horse meat scandle was such a problem in the UK.
Horses are like cars that can be happy to take you somewhere. And you don't disrespect an American's automobile. We'd eat sausages made from horses that died normally, but slaughtering one for meat is like burning a car just to get warm on a chilly evening.
There's also the potential problem of former racehorses, pumped full of performance-enhancing drugs, contaminating the food supply with their pharmaceutically tainted meat.
It definitely isn't because horses are smart. It may be because some of them are movie and television stars, a few are star athletes, some are considered pets or companion animals, and many are considered tools or co-workers. They don't have great brains, but they do have personality, even if much of that has been supplied by popular culture rather than actual contact with the animals.
Americans don't eat their dogs and cats, either. Some of them are dumber than a sackful of hammers, but you just don't eat family.
Beef? Cows won't fit in the house. Bulls are dangerous.
Pork? Most pigs turn into big fat jerks when they hit maturity, then they grow heavy enough to be dangerous. Also, they dig up everything they can smell, and are not overly averse to offal and excrement.
Chicken? Chickens are non-mammals, so it's harder to project our mammalian attachment behaviors onto them.
Deer? If they wanted mercy from me, they would have stayed out of all the gardens I have ever planted. But I also know people who won't eat venison because of Bambi.
We just won't eat foods that have the wrong narrative. Horses have Mr. Ed, Trigger, Silver, Satan II, Secretariat, Flicka, that one you rode at summer camp that one time, Epona, mounted police horses, the Budweiser Clydesdales, etc., etc., etc. There's even a literary trope where the named horse character has more "common sense" than its rider.
Personally, I've spent essentially no time around farm animals, but from what I understand about the scientific work in the area it seems likely that many farm animals have quite sophisticated minds. One review of experimental findings in pig intelligence[1] claims that "pigs possess complex ethological traits similar, but not identical, to dogs and chimpanzees".