The North Pole Hat of Warmth is a reward after reaching the North Pole.It can not be dyed or made.This hat cannot die out. You can, however, create some in a portal chest.
Seems to keep you warm in cold areas. Like the South Pole Boots of Speed, the Sunrise Hat of Fullness and the Sunset Skirt of Happiness, it can't die out. You have to go North until you find it. Make sure you're blockheads are wearing a Fur Coat and Fur Boots.
This is found on top of the North Pole. Use other blocks to reach it. You can't climb it.