The Christmas Hat (AKA Santa Hat) protects you from the cold the same as a coat but are only good due to how common gifts are. This is an upgrade from the Elf Hat which also comes from gifts.
The Christmas Hat is very helpful early to mid game, because it actually provides more protection from the cold than the Wolf Chapka (coat), and only slightly less than the Cap & Scarf. It is as warm as a winter peasant, winter hood, or pilot hat, although it does not give any protection from blizzards. This means that many experienced players, if they get this item, simply decide to choose it over making the Cap & Scarf because of its ease to obtain.