Is the horse from black beauty still alive?

Yes, still alive

Black Beauty was played by a Quarter Horse stallion named Docs Keepin Time, who played the role of another famous fictional black horse - The Black in Adventures of the Black Stallion. Black Beauty was also played by few other horses throughout the movie including a Saddlebred mare and Fresian as well.

Docs Keepin Time is a black American Quarter Horse most famous for starring as Black Beauty in the 1994 film adaptation of Anna Sewell's novel. He went from having an unsuccessful racing career to being one of Hollywood's most sought after equine performers. Docs Keepin Time also played the part of the rearing horse in the Busch Beer commercials, portrayed The Black in the American television series Adventures of the Black Stallionand Gulliver in the film adaptation of The Horse Whisperer.