First off, No, no Paul Roma. He gets put in with Kendall Windham and Hacksaw Butch Reed and Steve McMichael as "We don't talk about those guys". Chris Benoit we don't mention, but for other reasons.
The original Horsemen were Flair, Ole, Arn and Tully with JJ Dillon.
Lex Luger came later after Ole was cast out.
Then the Luger/Windham switch gave us possibly the best iteration (and the ine inducted into the WWE Hall of Fame) Flair, Arn, Tully and Barry Windham.
Fun Fact, Charlotte isn't the only child of a Horseman to be currently competing in wrestling. The lovely Tessa Blanchard is currently working her way up he indie ranks.