1) Implementing a simple system where you can attach a non claimed horse to your character, with a simple right click. A horse claimed by someone could not be claimed by someone else sort of deal.
2) Claiming a horse will prevent anyone else from riding that particular horse, when you claim a new horse the old horse will be left without an owner.
3) Hearth Magic that if the horse is lost, it will use the follow function to come back to you, which ever way is easiest, teleport to you, etc. Personally the follow function would be more realistic considering if he is across a lake he wont be able to get back to you, so he will only be able to get back to you if you haven't completely abandoned him and are not at least on the same land mass.



4) Perhaps create a map icon for claimed horses