Video demo of glitch: http://youtu.be/b5IQIMDJa1k

Behavior: Rider positioning is glitchy and horse is invisible after teleporting a horse to a new location. Player can move properly only after dismounting. Horse reappears only after player leaves the area and coming back in (probably fixes the horse during chunk reload).

Steps to reproduce:
1. Have a saddled horse and two clearly identifiable overworld teleport locations with coordinates jotted down on a notepad. Coordinates should be far enough apart to be outside of view render distance; a few hundred blocks will do. Single player game. Creative mode and survival mode show the same bug behavior so it shouldn't matter what you're in.
2. Mount the horse.
3. /tp @e[type=EntityHorse,r=3] x y z
4. Rider appears on the other end on the ground rather than mounted. Horse is not visible. Horse is still nearby and its breathing sound can be heard if you listen for a while.
5. Hold down w to try to run forward. Positioning keeps snapping back to the landing location, not letting the player actually go anywhere. Flying does not work at this point. View from various F5 perspectives confirms the weird movement constraints.
6. Press the left shift key. Dismount animation plays. Player is now free to roam around as usual. Horse is still not visible.
7. Teleport yourself far away and then back to the place you dropped off the horse.
8. Horse is now visible and behaving normally.

This is absolutely repeatable and consistent behavior for me, at those larger coordinate distances. Behavior is different over very small distances (20 or so blocks, easily within the view window).

I searched the bug database for all open tickets (reviewed by hand) and then also for closed tickets (keywords teleport and/or horse) and did not see any exact duplicates of this bug.