I was chopping trees while my horse decided to walk between the tree and my axe...
Anyway, what about that: when you hatch a horse, you get a piece of the egg, let's say with a hoove-imprint or whatever, in your inventory. It signifies that you own the horse, like it always follows the one with it's shell. Also, the name of the one who hatched it should be saved and displayed in the right-click-infos. Now you could even trade the piece of shell, and whoever has it is concidered the owner - so nobody could really steal your horse, maybe abduct it, but never claim it as his own...
Oh, and you shouldn't be able to sell the shellpiece in shops... no, no eating your pets x_X