While I don’t particularly like the term “Heart Horse” either, primarily because it seems (to me) just another trendy adjective, I most certainly relate to what that description should mean.
I’m one of those apparently not too bright owners with inferior horsemanship skills because ta da - I did have a horse I loved more than anything else in the world with the possible exception of my two children and my sister. I would gladly give everything I own to have that horse back.
He’s been gone for 10 years now. Where does the time go? I still miss him every single damn day!
I’ve had several very nice horses since that I enjoy and appreciate for what they are. They make me happy. If they didn’t they’d be on someone else’s dime (actually closer to $1,500/month).
They get the best feeds & hay (and plenty of it!), regular vet & farrier care. They are groomed, if only lightly, everyday. I am at the barn 2x/day to feed and inspect them even though I work full time (and the drive is 25-30 minutes each way). They are boarded at a place that doesn’t have all the riding amenities but has great turnout.
And while I care about each and appreciate them as individuals, I don’t consider any a “heart horse”. That type of connection comes maybe once or twice in a lifetime. Call me an old fool if that makes you feel superior but that’s my story and I’m sticking to it. 