The Catcher in the Rye "Madman"
by J.D. Salinger

Holden uses the word "madman" commonly as an adjective and in a variety of ways ranging from "[snow] was still coming down like a madman" to "I went right on smoking like a madman." It seems plausible that Salinger wished to convey that there is a bit of madness in the way Holden sees the world. The fact that the word comes up most often when Holden is criticizing himself could be a sign of further self-estrangement from society.