The 60-year-old Cone credited Winter for the influence he had on his career as a coach.
Former Bulls forward Scottie Pippen, who was also part of the six championship campaigns, shared how Winter made them run the flawless triangle offense.
Winter has been inducted into several basketball Hall of Fames, including the National Collegiate Basketball Hall of Fame in Kansas City and the Naismith Memorial Basketball Hall of Fame in Springfield, Mass.
In 1999, Winter followed Jackson to Los Angeles, where the triangle offense became the cornerstone of a Lakers team that won three championships from 2000 to 2002.
After 38 years of coaching college basketball, Winter began his NBA career with the Houston Rockets in 1971 before joining the Bulls in 1985.
"Tex Winter was a basketball legend and perhaps the finest fundamental teacher in the history of our game".
CHICAGO, UNITED STATES: Chicago Bulls coaching staff during the first game since the loss of Michael Jordan, Scottie Pippen, Dennis Rodman and coach Phil Jackson. "In addition to his numerous contributions to the game of basketball, Tex was a wonderful man and he will be dearly missed".
"Today is a sad day for not only Kansas State University but also the entire basketball world with the passing of Coach Winter", K-State athletic director Gene Taylor said. "He transformed the game of basketball at all levels and will always remain an integral piece of our rich basketball tradition here at K-State". "Our thoughts and prayers go out to the Winter family". "However, he left a tremendous mark of achievement at Kansas State, including two Final Fours".