Dude, Where's My Horse?
Solution 1:
Sounds like a bug. Pickpocket him to get your money back and try again.
Solution 2:
It's a bug, and doesn't seem to go away with save reloading or game restarting. However, you may not own the horse at his stables, but if you fast travel somewhere, your mount may show up. It may only show up if you fast travel to a different stable.
Solution 3:
Let your body wander to a different location and your steed might find you. (try fast travel)
Solution 4:
I would suggest reloading a previous save and trying again, I've found that it somtimes fixes bugs similar to this. If this does not work, reload once again and buy another horse from a different city.