In my first save with the Horse Ranch expansion, I had my horse into a big fenced area that she couldn't leave, and I think that helped "containing" her and avoiding some of the spontaneous interactions.
In my new save, I left my horse free to roam around the lot, and I noticed that sometimes the game queues social interaction with the horse, but I haven't noticed them being that disruptive of my game, even if my horse is needy. Now I have added a second horse to the family, and the two horses interact a lot with one another, so maybe you can try that too and see if being busy with another horse divert the other horse attention.