Been a while since I did my art history -- and from what I remember, the old code about horse sculptures has been muddied as many sculptors entered their art outside of the Academies and Formal Schools. (That is, some sculptors have followed the code from the past whilst others have chosen to break or ignore the code. So take any modern sculpture -- especially New World sculpture -- "with a hefty grain of salt".)
Four legs on the ground meant a natural death or did not die in battle. If the sculpture had three, then the rider was allegedly injured in battle. And so on. Lack of a rider however had no real significance -- at least from what I remember.