This is a really well done short shooter, you've have nailed the feeling quite well. The shotgun feels situational, but was useful in the room that opens up with two yellow snowmen, that I noticed deal more damage. The aesthetic works really well. Cutscenes and in-game art feel suitably Christmasy. Santa is always prepared made me chuckle. Music and sfx fit the genre well. Nice addition of adding the yog music video snowman as a boss. Very solid submission to the game jam!
Edit: Looking at the screenshot and going back to the game, I appreciate the addition of a subtle attack animation where the snowmen close the "eye" opposite the side they're holding the gun as if they're aiming. That's good visual info for the player to recognize when the player is within their attack range.