This is technically Pia Zadora's first film; she's the martian kid furthest to the right on this poster. Her character is named Girmar and she's a sad little alien girl because there is no Christmas on Mars. After all, Santa can only take care of one planet at a time, right?
The Martians kidnap Santa, and before the film is over, he must bring Christmas to Mars, defeat the Martians who are opposed to Christmas, and get kid companions Billy and Betty back home to Earth. It was featured on Mystery Science Theater 3000 in one of their early seasons.
Links for Santa Claus Conquers the Martians: