Corporal Snodgrass was a member of Company M, 3rd Battalion, 38th Infantry Regiment, 2nd Infantry Division. He was listed as Missing in Action while fighting the enemy in South Korea on 12 February 1951. He was presumed dead on 15 February 1954. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Snodgrass was awarded the Purple Heart, the Combat Infantryman's Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.