Per Wikipedia this is the history of the song: In 1944, Frank Loesser wrote "Baby, It's Cold Outside" to sing with his wife, Lynn Garland, at their housewarming party in New York City at the Navarro Hotel. They sang the song to indicate to guests that it was time to leave.
Garland has written that after the first performance, "We became instant parlor room stars. We got invited to all the best parties for years on the basis of 'Baby.' It was our ticket to caviar and truffles. Parties were built around our being the closing act.". In 1948, after years of performing the song, Loesser sold it to MGM for the 1949 romantic comedy Neptune's Daughter. The song won the 1949 Academy Award for Best Original Song