Arnie "Buck" Buckman was the president of the Horsemen in the 1980's. He had inherited the role from his father.
In the early 1980's The Horsemen took Wolf West on as a prospect in order to create a truce after a series of conflicts with the Wests and their associates. When his mother Rita was released from prison, she came to the Horsemen to retrieve her boy. Buck warned that the truce would be over if he left, and Wolf continued to stay with them.
After Phineas O'Driscoll attacked Cannonball, Buck went to Ted West's house to sort things. The two made a deal to let Phineas and Cannonball fight it out in the boxing ring. Cannonball won the match by way of disqualification after Phineas bit his ear and kicked him in the groin.
To honor a deal between Buck's mother and Rita West, Buck ended Wolf's time with the Horsemen with a final warning not to cross him in the future.
In the 2000's, Tyson had replaced him as Horsemen President.