after a quick look ...
if you look at the death and dying section of the Rules Compenium (or player's handbook), it talks about "when the player character goes below 0..." (emphasis added by me).
no where (that i've seen) in the monster manuals or DMG does it mention the same for nonplayer characters (which includes monsters, mounts, or even allied npcs, etc). Thus, I would say that a mount dies at 0 (not counting nonlethal damage).
The ranger's beast companion is given an exception to the rule, explicitly stating that it is treated as a player character for the purposes of being able to go below 0 into a dying state.
therefore, by raw, i'd say a mount (or any NPC, that includes allies) dies at 0.
However, this being an exception-based game system and DM having ultimate say-so, there is nothing from stopping the DM from saying the mount is an exception and follows the PC dying rules as well, which would let it go below 0.