Corporal Dexter was a medic with the Medical Company, 23rd Infantry Regiment, 2nd Infantry Division. He was listed as Missing in Action while tending his wounded comrades in North Korea on 1 October 1952. He was presumed dead on 31 December 1953. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Dexter was awarded the Purple Heart, the Combat Medical 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.