Apart from both sport using the same type of facilities, FS and hockey seem to be in a very opposite nature. Some skaters started with both before going full stream to their final choices. I just came across the article stated that Chan and Nyugen started FS to improve their hockey skills.
Brian Orser, who happened to have his name attached to one of the Hockey Arena, uses hockey power play techniques to improve skaters' speed in his coaching. Max Aaron is famously linked to hockey. Nathan Chen also involve in both sports.
On the other hand, figure skating happened to be a part of NHL players training in the recent years.