As shown in a video below, teleporting a horse far away while riding it, causes the player to float and unable to look anywhere other than up and down. Saving and quitting fixes the player, but the horse no longer exists even if you go to the coordinates.

Additionally, as of prerelease 5, teleporting any entities outside of chunks turns it invisible. You can still execute as it and it reappears when you teleport it again. If the entity isn't teleported again after turning it invisible, saving and quitting removes the entity altogether.