Snyder was an instant hit in Cleveland with his power, strong throwing arm, and matinee-idol looks framed by long, shaggy-blond hair. His father Jim had been a minor-league infielder in the early 60s with the Milwaukee Braves. A member of the 1984 U.S. Olympic baseball team, Cory was the fourth overall pick in the 1984 draft.
Snyder’s 24 homers and 69 RBI in 416 at-bats in 1986 earned him fourth place in American League Rookie of the Year voting. He was a third baseman and shortstop in the minors, but his poor fielding necessitated a move to right field, where he led AL outfielders in assists in 1988. He hit more than 20 home runs his first three seasons, with a high of 33 in 1987, and has hit as high as .272 twice. However, he soon revealed several flaws, including striking out frequently while rarely walking. In a 1989 game, Pete O’Brien was intentionally walked three times in favor of pitching to Snyder. Later that season, while hitting .229, Snyder went on the disabled list with a bad back.
Cleveland gave up Snyder him the next season after he posted a .270 on-base percentage, trading him to the Chicago White Sox with Lindsay Foster for Eric King and Shawn Hillegas. It looked as if his career was over when he batted just .175 in 1991, but his power stroke returned somewhat in San Fran and LA. On April 17, 1994 he joined Gil Hodges, Don Demeter, and Jimmy Wynn as the only Dodgers to hit three home runs in a game (Hodges had four). No clubs showed interest when he became a free agent after the 1994 strike year.