The novella does not state who repeatedly wins at horseshoes. In Chapter 5, Steinbeck does briefly describe that while Lennie is alone in the quiet barn with his dead puppy,
"from outside came the clang of horseshoes on the playing peg and the shouts of men, playing, encouraging, jeering" (84).
Throughout the rest of the pivotal chapter, Curley's wife and Steinbeck's narration references the "tenement" still going on outside, but neither states who is winning or who has won.
The Gary Sinise film version of the book does portray George as winning repeated games. Most likely, the screenwriter chose to include this to portray George at the top of his game--he is making friends, his farm dream is closer to realization than it's ever been, and he is successfully competing against the other ranchhands. George's high spirits contrast pointedly with his reaction when Candy shows him Curley's Wife's body.
In chapter three, we are shown that Crooks wins repeated games of horseshoes: "The thick-bodied Carlson came in out of the darkening yard. He walked to the other end of the bunk house and turned on the second shaded light. "Darker'n hell in here," he said. "Jesus, how that nigger can pitch shoes."
"He's plenty good," said Slim.
"Damn right he is," said Carlson. "He don't give nobody else a chance to win--"