I will say, it is definitely arbitrary why people have that feeling towards horses and not cows, pigs, sheep, etc. who are just as intelligent and worth our consideration

I think lot of it has to do with the fact that more people have grown up seeing how kind and sweet other horses are and it's not as socially common to eat them in the US. Because of all that people are able to see them as morally valuable and killing them as wrong

Whereas for other farm animals, people have grown up seeing their killing normalized and since it's normal it's not questioned. If you come from Europe or elsewhere where horse meat is more common, then you'll have also seen horse in the same way as other farm animals where their killing is a normalized thing