In advance: Make cookie hat. Prepare dough and roll out. Use pattern to cut hat; position on cookie sheet over cookie stick, leaving 3 in. of stick exposed. Bake and cool.
Bake and cool cake. Ice inside mouth and ears smooth. Use tip 5 to outline mouth and pipe in eyes and nose (smooth with finger dipped in cornstarch). Cover cake with tip 16 stars. Ice hat cookie smooth and print tip 4 numeral. Insert cookie on top of head. Pipe tip 14 pull-out pompom and hat fringe.