This has happened to me a bunch of times. There are free horses all over skyrim, just as there are free beds if you know where to look (not just bedrolls, but actual beds).
I don't think this is a spoiler, but there's always a free bandit horse behind whiterun from the beginning of the game. Go outside the gates, turn right, and follow the rocky perimiter as if making your way to the northern watch towers (whitewatch)
If it's the one I think you mean by the over-hang, it's marked as "steal" in my game. Shame.
Even if stuff belongs to dead people, you can take as much as you want off of their dead body, crime free. But take their food. Sleep in their bed. "Borrow" their PREVIOUSLY owned horse before they are killed (not neccessarily by you) and you are marked as a thief (ie you have stolen items from a dead person).
I wish the ownership flag would change (especially for a certain murderer in Windhelm after he's dead), so you could take over their horse, sweetroll, bed, whatever. Surely it would have been quite simple to impliment. (Though possibly glitch the game even more. But that doesn't seem to have been a major design concern so far, eh?

)
It may not be allowed because it may encourage people to murder for their items so that's why it hasn't been implimented. And we can't have Skyrim encouraging people to do horrific things like that now, can we...?
EDIT: Unbalance the game? Well, in regard to horses, the amount of horses I go through in one day due to their own 1000g's worth of intellect and desire to be Dragon fodder, bandit practice, Saber tooth tooth sharpeners or a giant's giant baseball, -especially right in the middle of nowhere, I think I know where the word "unbalanced" would fit in.
Failing any hope of the above, a "STAY!" command would be nice. But I guess even the dogs don't respond to that...
Sorry. A bit jaded today.