Mix together the powdered sugar and 1 1/2 tablespoons water in a small bowl until thick and smooth. Pour the icing into a piping bag fitted with a small round tip. Pipe 3 parallel horizontal lines an inch apart around the cupcake liners. Pipe vertical lines an inch apart from each other to create a brick pattern (this will be the "chimney"). Let set completely on a serving platter.
Transfer the white frosting to a pipping bag fitted with a medium round tip and pipe onto the top of each cupcake. Dust with desiccated coconut.
Skewer the red licorice candies with a toothpick, leaving 1/2 inch of the toothpick exposed on one end. On the exposed end, skewer a halved marshmallow, then a halved chocolate licorice to make the legs. Repeat with the remaining marshmallows and chocolate licorice. Place 2 legs onto each cupcake.