The summary describes it exactly, it's really simple. It's the only step. If I log off while sitting on a horse, the next time I log on it is gone. Like completely gone from underneath me. I can fly around and look for it; nothing.

Java 1.6.0_33-b05
(Version 6, Update 33. Said it last updated on Feb 14, 2014)

More details that may not matter, but I'll include just in case...
– It has only ever happened to me in this most recent version or minecraft... and maybe even Java. As far as I know it has only happened in the past few days. (I can't be more clear on the time frame, I wasn't really paying attention, but I know it's been the new version. ...Though I don't think I usually logged off while on a horse before so I can't say for sure if it would have happened at an earlier time in an earlier version of either.)
– I don't even know how to mod things so nothing is different or added to my version, I don't think. We had pixelmon added to our server, but now I'm not using a server. The game in question is on my personal computer that only I access.
– This seems really pointless to say but it happens to donkeys too.
– I can be leading other horses too and the only one that disappears is the one I'm sitting on. And I mean, the others I'm leading are exactly where they were the moment I logged off, like they should be.
– I've been in really safe, solid, areas when it's happened.
– It happens in both survival mode and creative mode.
– I have not tried to reproduce it in other world/seeds ...because I only just thought of that now.
– I like to breed horses to get good ones; so I have a lot. It's also a naturally horse heavy seed too. I'm guessing around 300-400 the one, large, main, map area.
– But the problem has also happened when I'm several maps away from that heavily horse populated zone where there are not a lot of horses or even other animals. (Like in a HUGE "winter plains?" -forgot the name of the zone type... where there is practically nothing. It takes up half the map)
– It's happened with bred ones I've had for a while and I think it has also happened with naturally occurring ones. Even the naturally occurring ones that I was taking back "home" from long distances. (ref: like over that "winter plains" area)
– I've only lost track of two other horses, ever, in hundreds of hours on this world, and they were loose in the world and I kind of think they may have drowned when they were slightly out of eye site and earshot. (They all have name tags.) Like, I saw them hovering around my castle moat and they may have just gotten stuck underwater. So.....
– I can't be 100% sure but I honestly don't think ones I'm not riding have ever non-legitimately disappeared. Just the ones I've been on.

I can't think of what else to say. But, ah, 2 of the horses I lost this way were so amazing. THE TRAGEDY. But, seriously, it freaks me out a little because I just spent a few weeks finishing an amazing stable to house them, and I'm worried about screwing up again or find out other ways they might disappear. (I'm a little too much into creating the perfect horse line, breeding them, testing them, and finding good wild ones has been kind of like crack for me. I haven't been doing anything else in the game in ages. Thanks for adding horses, btw! ~I've had so much fun with them! Now add whales heh heh )