Although Centre was known as one of Kentucky's foremost colleges, Cooper's father wanted him to broaden his education and, after one year at Centre, Cooper transferred to Yale College in New Haven, Connecticut. At Yale, he was a classmate of his future U.S. Senate colleague, Stuart Symington. Cooper was active in many extracurricular activities at Yale, including the Sophomore German Committee, the Junior Promenade Committee, the Student Council, the Class Day Committee, the Southern Club, the University Club, and Beta Theta Pi. A member of the Undergraduate Athletic Association, he played football and basketball, becoming the first person in Yale history to be named captain of the basketball team in his junior and senior years. In his senior year, he was accepted into the elite Skull and Bones society but regretted not being accepted into Phi Beta Kappa. Upon graduation, he was voted most popular and most likely to succeed in his class.