The Winter Hat was used to start a snowing effect, with no practical use besides the visuals. This effect was removed as of the A Winter's Tale update, when winter became a feature. Its crafting description during this time was "There must be some magic in it...".
The Winter Hat used to cost 100 points under the old Research Points system. Adding it into a Science Machine or Alchemy Engine would give the player 10 points.
Klei Entertainment made a new product themed after the winter hat. It also comes in pink and grey versions, which include codes to unlock the corresponding colored Winter Hats in Don't Starve Together.