In Oblivion you got arrows in you inventory from enemies shooting at you.
Perhaps the horse got them in forsworn territories and kept the arrow for an long time,
Or as Rexx says, it might come from followers the same way.
Highly doubtful that my follower shot the horse and put a Forsworn arrow in it, as I regularly dink around in my followers' inventory for misc. reasons, and chuck out any crap arrows like that she occasionally ends up with. And it had been a long time since I'd last been in Forsworn country. The most likely explanation is the one about the horse getting shot with one way back the last time we were in Forsworn country, and keeping it in its hidden inventory until it died. Wasn't aware that could happen, but it's the most logical idea so far. Considering there were no dead enemies nearby, which there would have been if they had been taking on Jenassa and my horse (Jenassa kicks serious booty), it was probably a heart attack.
I've seen my horse keel over and die in place from full health to nothing in a millisecond before, so I know it can happen. And with no combat going on nor any enemies nearby. Couple other times since I've been playing, I've come back to a similar scenario with a dead horse and no evidence at all of why- with a whistling follower and no enemy bodies anywhere. Maybe Jenassa just doesn't like horses... or is jealous that I am riding and she has to trot along behind... perhaps she killed it and stuck the arrow in it to throw me off... gonna hafta keep an eye on that one.