I think this is an interesting question.
My definition of a heart horse is that the horse and I “click” and we read each other very well. I’ve had two heart horses and they trusted me more than anyone else. One of them I rode for three years and never had a single problem, yet she spooked with other riders and could be stubborn. She had a severe pulling back problem and couldn’t be tied, yet for me she’d stand quietly anywhere I placed her (without tying). If someone else tried to place her she’d walk off. If I slapped my leg twice she’d follow me, I never officially trained her to do that, it just sort of happened. She never showed any signs of affection, but the exceptional communication was there. It took several months to reach that point, and I really loved her.
My Icelandic, I knew after my first ride that he was going to be a heart horse. When he was upset about something he’d flip his lip at me, he didn’t do this to anyone else. I quickly learned that I needed to do something when he flipped his lip. I was the only one who could touch his ears. When I arrived at the barn stressed out from work, he’d give me “pony kisses”, i.e. wiggling his nose on me. I will always miss him.
I don’t think you can create a heart horse, much like you can’t create a best friend, it just works out that way. If a horse actually “didn’t like me”, i.e. we didn’t “click”, I’d probably sell it to someone who was a better match. This actually happened to a friend who sold a really nice hunter because it just didn’t work between them. The new owner is happy and the horse is performing better.
Animals have personalities and sometimes they click with ours. Much like people, we may have lots of friends, but only a few are best, closest friends.