I bought my first horse from Whiterun. Had it for some time but it ended up dying during a dragon battle. I went back to Whiterun to buy another horse but the horse vendor there had no option for me to buy another horse. So I ended up buying another horse at a second city (can't remember which).
Fast forward about 10-15 real hours playing Skyrim, and my once-dead horse is alive and well at the Whiterun stable. Is this normal? That horse was dead, no mistaking it.