I accidentally killed my first horse, so I bought a lovely Palomino from the stable outside Solitude. One day, I was fighting some battle and I couldn't find my horse so I assumed it had been killed and I just couldn't find the body. So I went to another stable and bought a pretty paint horse. A few playing days later, I found my Palomino, just hanging out in some field I'd never been to. Now instead of saying "Ride Arwen's Horse" it just said "Ride Horse", but not "Steal Horse", so I was pretty sure it was mine. I got on the Palomino and went back to Whiterun, where I have a house, and thought I would just travel without the horse back to where i left the Paint, bring that horse to another town, and he'd hang out in their stable and I'd have two horses to choose from. But that didn't happen. When I returned, the Paint was gone. So, question 1: what happens if you own two horses? Where do they go?
So I'm riding the Palomino around and eventually ended up losing him, but I thought he was dead so I went to buy a new one. I went to the Solitude stables because I happen to be partial to Palominos, and the guy took my money, said "it's all saddled up" but the horse was not there! There was only 1 horse, it wasn't saddled, and the only option was "Steal Horse". I was kind of mad that I lost 1000 gold pieces! I realized too late that my horse must not be dead. So, question 2: is there some way to confirm whether your horse was killed other than spending 1000 septims on a horse that isn't there?
My final tale: I lost my Palomino horse again (and this time I knew I hadn't killed it by accident) and had to fast travel several times all over the map, wait a few hours on more than one occasion, and then suddenly it showed up. But the weird thing is, after I rode it, I got off to fight a wolf or something and the horse wandered off! Every time I got off it would leave as if it were returning home (it didn't use to do that). So I lost the damned thing again when I stopped to kill a dragon. I miss my horse! Question 3: What can I do to make sure it follows me around to the various stables in the cities I visit?