Chill cake in pan for 30 minutes to set the top. Spread ice cream evenly to the pan's edge. Freeze for several hours until the ice cream sets.
Unmold the cake from the pan. Spread frosting around the sides of the cake and create a 1-inch border on the top. If the ice cream starts to soften, place the cake back in the freezer.
Drizzle decorating icing in a crisscross pattern over the top of the cake. Arrange sugar sticks diagonally around the sides (omit bent tips if using candy canes). Scatter cherries around the top of the cake. Chill in the freezer for several hours or overnight before serving.
Moisten marshmallows with water and coat in sugar crystals. Add pretzel sticks to create 'drumsticks'. Place on cake before serving.