Are you sure that horses are not able to teleport? In Minecraft PE everything is possible! Try the new kind of mounts provided by Ender Horse Add-on!
Ender Horse Add-on changes not only the appearance, but new horsed look pretty cool for us. The taming process has no difference – you just need to sit on it and wait for hearts to appear.
However, nothing is perfect. Ender horse is much faster than vanilla Minecraft PE mount and it is able to jump higher (five blocks), but teleport may disappoint you a bit. Players cannot chose the location to teleport: it means that your journey may became even longer, if your mount is teleporting back. Moreover, the baby ender horses cannot teleport at all. By the way, they are very strong and have 33 hearts, so these mounts can absorb part of fall damage.
1.2 beta (scroll down for 1.1 and below):
Published: Kukusya; Category: Addons for Minecraft PE; OS: Android | iOS