After the 1954 NFL season, Davidson received word that he had been drafted by the U.S. Army. He served in the Army for two years and did not take part in the 1955 NFL season or the 1956 NFL season. By the time Davidson returned to the Colts for the 1957 NFL Season, John Unitas was the team's starting quarterback.[1]
While in the military, Davidson played quarterback for the Fort Bliss Falcons from 1955 to 1957. A game between the Fort Bliss Falcons and the Cannonneers of Fort Sill, Oklahoma, was played for a trophy called "The Little Brown Dud." The Cannoneers won the game and took home the Little Brown Dud. Cotton was awarded All-Army Quarterback in 1955.
After the 1962 season opener, he was traded to the Oakland Raiders for the first overall selection in the 1963 American Football League draft. Just two weeks later, Davidson started at quarterback in his first game with the Raiders. Playing against his former team, he threw for 248 yards and rushed for a touchdown in a 26–16 loss to the Texans.