Head to the North Pole and enter the Toy Factory at (9,11).
In Toy factory walk to (18,6) and enter Santa's room.
In Santa's Room walk to (12,0) and enter Raindeer Pen.
Speak to Elf and he will tell you that Rudolph has escaped and that he will be in big trouble if Santa finds out.
Agree to help him then head back outside and kill Snowmen until you receive a Rudolph.
Take Rudolph back to Elf and he will give you instructions on how to receive your reward.
(Make sure you don't have Rudolph equipped or he can't take it.)
Go back outside and say "Merry Christmas" to the tree to claim your reward.