I am pro slaughter, because a horse is a huge great big ticket item, that takes a lot of space and inputs to keep it happy and healthy, I believe that if it can't be kept happy and healthy, then as a large herbivore, then there is meat that is useable there, shame to waste it really.
Dogs and cats are a little different, smaller animal, takes up a smaller space, doesn't need quite so many inputs, all things being equal, and as a carnivore, then not quite so attractive as a food item.
Being horribly practical, it's a lot easier to dispose of the remains of a domestic pet, I mean you can flush a Goldfish, but a horse, well that is a plumbing problem you don't want to contemplate.
My own view, is not life at all costs, but a quality of life. If the quality of life can't be maintained, then a quick and merciful death, and I do believe that it should be both of those things, but honestly once life has departed, then carcass disposal is a whole nother thing....