A Bay Horse is one of several horses found in The Elder Scrolls IV: Oblivion. It can be considered a step up from the Paint Horse with more speed, but less Health. Even though it's not as fast as the Chestnut Horse, it does have more health than it.
Bay horses can be purchased at either Bay Roan Stables near Bravil or Grateful Pass Stables outside Skingrad for 1000. It should also be noted that the Bay Horse has the same statistics and appearance as the Imperial Legion Horse.