Steps to reproduce

Part I, with horse

1. Load https://bugs.mojang.com/secure/attachment/550787/MCPE-170425.mcworld
2. Ride the gold horse into the nether portal, dismount, and wait to be transported to the nether.
3. Once in the nether, place a boat on the longer ice path and ride it to the end.

Part II, with any mob

1. Load https://bugs.mojang.com/secure/attachment/550787/MCPE-170425.mcworld
2. Go to overworld 0 58 -14.
3. Spawn a passive mob and push it into the portal
4. Go into the portal.
5. In the nether, place a minecart on the minecart track and push the mob you spawned earlier into the minecart.
6. Push the minecart all the way down the track to the other end. (Takes a few minutes.)
7. Break the minecart to release the mob.
8. Push the mob into the nether portal at -416 18 -352.
9. Go into the nether portal.
10. Wait for the mob's portal cooldown to expire, then push the mob into the portal on the overworld side.
11. Once in the nether, place a boat on the longer ice path and ride it to the end.

Expected result

When you load into the nether at -419 18 -349 the gold horse from Part I or mob from Part II is there with you.

Observed result

You find the gold horse from Part I or mob from Part II near the portal at -6 18 -16.