Cone grew up in Pine Apple, Alabama, with a population around 100. He attended Moore Academy, a one-room school from kindergarten through high school. He didn't play football because there weren't enough people to field a team. Before going to college, he enlisted in the U.S. Army to take part of World War II, where he served in the Pacific as part of the 11th Airborne Division.
College career
When he returned to the United States in the summer of 1946, he read a newspaper advertisement about tryouts at Auburn University and decided to attend. His participation was cut short with an ankle injury that forced him to return home. During his recovery, a family friend turned out to be the sister of Frank Howard, the head coach at Clemson College. She helped Cone get a tryout and eventually he was able to make the team and receive a scholarship. Cone was the starting fullback in a backfield that included Ray Mathews. The 1948 team finished undefeated and beat the University of Missouri, 24–23, in the 1949 Gator Bowl. He scored two first-quarter touchdowns and had a critical fourth down conversion late in the game. The next year, he registered 703 rushing yards and 8 touchdowns. As a senior, his 184 carries for 845 rushing yards, 15 touchdowns and 92 points at the time were all school season records. He also was a part of another undefeated season and played in the 1951 Orange Bowl, beating the University of Miami 15–14. He gained 81 rushing yards, scored one of the touchdowns, returned one kickoff and had 4 punts. He finished his college career with eight 100-yard career rushing games, 31 touchdowns and 189 points. He also was a kickoff specialist. In 1973, he was inducted into the State of South Carolina Athletic Hall of Fame and the Clemson Athletic Hall of Fame. He is a member of Clemson’s Ring of Honor.
Cone was selected by the Green Bay Packers in the third round of the 1951 NFL draft. He was used as a fullback and placekicker. As a rookie, he led the team with 50 points, and was the second-leading rusher with 56 carries for 190 yards. He also made 5 of 7 field goal attempts and 29 of 35 extra points. Cone led the Packers in scoring in five of the next six seasons, including leading the league with 16 field goals made in 1955. The next year, he announced his retirement, but was eventually convinced by the team to return. In 1957, he was a part of the inaugural game at Lambeau Field, then known as City Stadium, contributing to an upset of the Chicago Bears 21-17, before a crowd of 32,132 people. He finished the season by leading his team in scoring with 74 points. He played for the Packers during a low point in the franchise history, never experiencing a winning season, which cost him the opportunity to earn more accolades for his play. In 1974, he was inducted into the Green Bay Packers Hall of Fame.
Dallas Cowboys
On May 12, 1960, he was signed as a free agent by the Dallas Cowboys after being out of football for two years, while coaching at University Military School in Mobile Alabama. He became the first starter at placekicker in franchise history. He also was a backup fullback and reunited with former college teammate Ray Mathews. He was released on August 28, 1961.
Personal life
In his first two years in the NFL, he worked for the Packers during the offseason promoting season-ticket sales. He later accepted a job promoting beer with the Miller Brewing Company. He also worked for the Clemson athletic department as their chief football recruiter in the 1960s. Country comedian Jerry Clower, who played football at Mississippi State University, recounted his experience facing Cone on the field in his story "The Time We Played Clemson".