Though this bug was fixed in a snapshot, horses once more despawn when playing on a Survival Multiplayer server. The effect affects all players on a server, with horses disappearing either all at once or one at a time in different parts of the server. On the server I play on, in particular, EVERYONE lost their horses. Every single player with horses, some with a large stable of ~dozen, lost all of them.

The bug appears to be linked to the amount of players online, as well as the chunks the horses are in being loaded and unloaded. According to reports around the web, it also appears to be widespread and happening across most servers. It's kind of critical that it get fixed quickly, as it means no one can have horses.