The music was perfect! And I liked the popping sound effect when shooting.
I like that you provided a little story as well!
My biggest piece of feedback would be making the player and snowman move at different speeds (I think that was the issue I was seeing?). I would try to move left-right in order to line up with the snowman to hit him, but we moved at the same pace so I couldn't align my shot.
Also, a kill count would be nice to gamify it a bit more (try to beat the high score).
Good work!