I knew someone who had a horse alone at home, and thought the horse was perfectly happy. There wasn't anything you could point out and say "that horse is lonely." But, she later ended up moving her to a boarding barn for other reasons, and realized how much better
the horse was doing being around other horses. I think some horses do OK with no horses (or farm animal companions) but that even these horses do better with companionship. It doesn't necessarily need to be a horse, but they do need something (goat, cow, sheep, etc.) there with them.