1985: two-year-old season

Conditioned by veteran California trainer Mel Stute, Snow Chief made nine starts at age two, winning five, including the Norfolk Stakes and the Hollywood Futurity. His 1985 performances earned him California Horse of the Year honors, but Tasso, the 1985 Breeders' Cup Juvenile winner, was voted the Eclipse Award for American Champion Two-Year-Old Colt.

1986: three-year-old season

As a three-year-old, Snow Chief made a further nine starts. In California, he won two stakes races, then was sent to Florida, where he won the important Florida Derby. Back in California, he established himself as the solid Kentucky Derby favorite with a win in that state's most important race for three-year-olds, the Santa Anita Derby.

Snow Chief was sent off at even money as the bettors' choice in the Kentucky Derby but in a sixteen-horse field, he finished eleventh to winner Ferdinand. However, Snow Chief returned to form in the Preakness Stakes, defeating runner-up Ferdinand by four lengths.

His handlers chose not to run him in the 1½ mile Belmont Stakes. Instead they later sent him to Garden State Park, where he won the Jersey Derby. For his performances in 1986, Snow Chief was named California Horse of the Year for the second straight year and was voted American Champion Three-Year-Old Male Horse.

1987: four-year-old season

Snow Chief returned to racing as a four-year-old in 1987. From six starts, he won two and earned three seconds. His wins came in the Charles H. Strub Stakes at Santa Anita Racetrack in California and the Oaklawn Handicap at Oaklawn Park Race Track in Arkansas. He was voted California Horse of the Year for the third time.