The 27-year-old Quinn, who could be a backup to Matt Cassel for the 2012 season, hasn't appeared in an NFL game since 2009 with Cleveland. He was on the bench as a backup for Denver last year.
During his career, Quinn, a first-round pick of the Browns in 2007, has completed 184-of-353 passes for 1,902 yards with 10 touchdowns and nine interceptions.
Winston, 28, a strong right tackle, was a third-round draft pick of the Houston Texans in 2006. He hasn't missed a contest in each of the last five years.