Cozier attended University of North Carolina at Charlotte, where he played on the men's team from 1992 to 1995.
The Columbus Crew of Major League Soccer selected Cozier in the first round (tenth overall) of the 1996 MLS College Draft.
[2] In 2004, he was named to the second-team USL All-Star team after scoring goals in games with Atlanta.
Cozier played one game with the Columbus Invaders during the 1996–1997 National Professional Soccer League season.
Cozier, along with several teammates that day, was called up when the regular national team players went on strike and refused to play.