When I was a little kid, and the Christmas tree was decorated and up, and maybe the presents were under it, my sister and would sit under the tree, and imagine that it was a world unto itself.
That made me think that it could be cool to have a videogame that took place in a Christmas Tree. Logically, it seems the most straight forward way of making a task out of that would be to start at the bottom and work your way to the top. Possibly the goal there could be to light the star at the top. For a slightly "darker" theme, the angel at the top could have been kidnapped, and now an evil Dark Angel sits at the top of the tree, and is the game's final boss.
I visualize the game as a 3D platformer. If the game goes from the bottom of the tree to the top, then, to incorporate some Christmas Tree theme into it, near the top, where it's narrow, stages could be wrapped around the tree, like a 3D version of the tower in Battletoads.
Lower on the tree, where the tree would be broader and could extend quite a ways, the stages could have just about any layout imaginable.
The Christmas tree layout could suggest a few obvious themes for settings, but aside from green, and lights, and bulbs/balls, my favorite Christmas tree ornaments as a child were the more distinct things: Angels on clouds, skiers, stained glass. These could be incorporated into the game in various ways. Just off the top of my head, there could be "minigames", so skiing with the skiier could be like sliding with the penguin in Mario 64. If an ornament had a scene inside, perhaps it could be entered, to add some variety to the settings.