Why does my horse break the lead I tied him to the rail with?
Solution 1:
It's a common problem sadly i dont think there is a fix for it you just need to wait for the next patch.
here is a forum post about it http://www.minecraftforum.net/topic/1884637-163-one-major-thing-they-need-to-fix/
Solution 2:
Theres really no way to stop it at the moment (its a glitch and it just happens randomly) so I don't take chances and I just put my horses in a small room or even in the house. Monsters have also accidentally killed some of my horses so I just completely avoid leaving them outside unless in a fenced in pasture.
Hope this helps :)