Winkler was selected by the Miami Dolphins in the 10th round (82nd overall) of the 1966 AFL redshirt draft and by the Detroit Lions in the 12th round (178th overall) of the 1966 NFL draft as a "future" player.[1][9] He was one of several small-school players selected by the Lions; head coach Harry Gilmer, when asked Tarleton State, said that it was "Somewhere in Texas, I think".[10] In December 1966, at the end of his college career, Winkler signed with the Lions, becoming his school's first-ever NFL player.[11] He suffered a sprained knee shortly prior to the 1967 season and began the year on the taxi squad, before a promotion to the active roster in October 1967.[12][13] Winkler then appeared in eight games for the Lions as an offensive tackle in 1967, all as a backup.[1]
Winkler was released by the Lions at the start of the 1968 season, then later joined the taxi squad for the Atlanta Falcons.[14][15] He later was promoted to play guard for the Falcons, appearing in 12 games, four as a starter, during the 1968 season.[1] In June 1969, it was announced that he was drafted to serve in the United States Navy Reserve, making him unable to play that year.[16][17] He served two years in the Naval Reserve and during that time worked as the offensive line coach for the Navy Midshipmen football team.[17]
After leaving the Navy in 1971, Winkler returned to the Falcons, but was released in favor of several younger guards.[17] After not being claimed by any team off waivers, he contacted the head coach at Navy, who then called several NFL teams.[17] The Green Bay Packers became interested in Winkler as a result and signed him in August 1971.[1][17] Initially on the taxi squad, he was called up to the active roster prior to the team's game against the Minnesota Vikings, replacing an injured Dave Bradley.[17] He posted a tackle in the game while appearing on special teams, in what was his first NFL action in two and a half years.[17] He played in seven games, all as a backup, for the Packers in 1971.[1] Winkler was released prior to the 1972 season, ending his professional career.[14] He finished with 27 NFL games played, four as a starter.[1] He was inducted into the Tarleton State Athletics Hall of Fame in 1981 and to the Belton High School Wall of Honor.[2][8]