Whether to buy or not to buy has been a topic for much debate, but if you do decide to buy, I wanted to provide a small heads-up. Don't leave your horse outside the back entrance (near the water) to Solitude and then go about your business inside. Not sure if it happens every time, but I popped into Solitude via the back entrance for just a few in-game hours and when I came back out, the horse had gone. There are no enemies in this part of the world (none that I could find) and I searched a decent space around the entrance to see if he had wandered off (to no avail).

Has anyone else experienced this?

Did you check the stables? Horses are supposed to go there when you Fast Travel to a city. Perhaps loading the Solitude Cell is enough of a trigger to make the horse go to the stable.