You get Santa Claus after defeating the Frost Legion. Can you get him if he dies AFTER the holidays, and will he available the NEXT holiday?
He's available every year during the holiday season (defined as December 15th - December 31st). Outside of this time frame, he dies the instant he spawns.
If you've already defeated the Frost Legion, he will respawn at the end of next year, provided you've defeated the Frost Legion on that world.