This bug is irritating. Reasoning: I found a rare horse, a speedy and a jumper. It had a saddle on it and diamond horse armor, both difficult to get. I get off the horse, re-log, it vanishes. I stay on the horse, re-log, it still vanishes. Please fix this bug, I'd rather not lose a third horse.

Edit: It also affects Singleplayer worlds, without the LAN.
Edit 2: Notice in the screenshots the zombie attacking what would be me on an untamed horse. I swear, the weirdest thing I've seen yet. Also the inability to get on the armored horse, and the armored horse acting (affecting me) as if it weren't there in the first place.