Green’s Dictionary of Slang

(Aus./US) a horse or human runner who is at their best on a muddy course or track.

1905		N.Y. Eve. Sun 17 Aug. (Cent. Supplement) n.p.: The third horse, Atholone, is by Handsel, a mudder himself and a son of a mudder [DA].
1917		Van Loan ‘The Last Chance’ in Old Man Curry 114: You’re forgetting that Last Chance is by a mudder out of a mudder.
1943		D. Burley N.Y. Amsterdam News 9 Oct. 20: [He] wanted her to weed him a holler note until his mudder came in.
1948		Time 1 Nov. 44/3: Halfback Jack Swaner, a superior mudder, had a big day scoring all three touchdowns [DA].
1953		A.J. Liebling Honest Rainmaker (1991) 46: The boys had a good spot for a mudder in the fifth race on the morrow.
1999		G. Seal Lingo 142: A mudlark, mudrunner, or simply a mudder is a horse that runs well in wet conditions.