Greenwood was known for wearing gold-colored shoes on the football field, to help announcers distinguish him from the higher-profile Joe Greene. Greenwood was called "Hollywood Bags" because of his desire to become an actor after retiring from football. He was a finalist in the 2005 Pro Football Hall of Fame voting but did not get elected. He was again a finalist in 2006, but was not elected. Greenwood has stated that while he would be honored if he were to be inducted into the Hall of Fame, he would not be upset if he were not elected, feeling that the Steelers already in the Hall (in particular, "Mean Joe" Greene) represent the entire team's accomplishments.