When teleporting a horse outside of loaded chunks whether you're riding it or not has different problems.

1.  When not on horse and teleporting it to unloaded chunks, teleporting there lets you see the horse for a frame before disappearing. Quit and reopen for it to appear again.
2.  If one the horse and you teleport both the player and horse at the same time it will occasionally only teleport the horse.
3.  Teleporting just the horse while riding it will sometimes freeze you in air. You can't turn your camera or crouch to get off. When going to the place the horse was teleported to afterwards, it is not there and can't be found.
4.  Teleporting just the horse while riding it can also result in the horse not teleporting and forcing you on the horse even if crouching for a little while before finally letting you off and not having the horse teleport.