There is always the possibility that the horse trips and breaks a leg while running away.

If that ancestor also can track it down, maybe.

You... probably not.

I don't think you could kill a horse in an open field without a long distance weapon. It's a flight animal, if you did any significant damage to it, you'd never come close enough to get it to fight you. Enclosed spaces, that's a different story (you still lose that, it's a horse).