Yes, it existed
Ski ballet became somewhat popular among skiers in the 1970s and eventually became a demonstration sport at the Winter Olympics in 1988 and 1992. A video of the event began circulating on social media this week.
The Olympics regularly feature demonstration sports to promote a new event. The International Olympic Committee must have been unimpressed with the trick-based event since they declined to make it part of the official Olympic roster.
This year: Synchronized skating
The demonstration sport this year is synchronized skating (or “synchro”). Like its cousin from the Summer Olympic, the judged event involves several competitors moving in unison to music. There are also several new official sports in Sochi, including team figure skating (which involves several normal figure skating events with a shared points system) and luge team relay.