It's a normal, freshly created reference. His "home" is the place he spawns at, which, in "normal" game, is the spot by the farm I built (or in case where I disable him and use the placeatme command it's the spot where he spawns), however normal horses you own in vanilla stay put when you dismount and they follow you when you fast travel. This one casually turns his ass towards me and goes back to his spawn point / farm spot. Didn't try fast traveling yet as I have that disabled, but entering/exiting interiors, like caves, isn't helping.
What I currently do is I disable the horse whenever I'm entering the city or an interior, and when I get back out I just spawn him with placeatme, but I can't imagine that to be healthy for my save file.