Beat together sugar and shortening. Beat in milk, egg and one tablespoon vanilla. Stir in flour, baking powder, baking soda and salt.
Shape dough into 1 1/4-inch balls. Place balls 2 inches apart on a baking sheet. Insert a stick into the side of each dough ball, and flatten with the bottom of a glass dipped in sugar. Bake at 350° for 8 to 10 minutes, or until cookies are golden. Let cool on baking sheet 2 minutes. Remove from baking sheet and cool on a wire rack.
In a small bowl, combine powdered sugar and remaining 1/2 teaspoon vanilla; add water, one tablespoon at a time, until spreadable. Spread frosting on top 1/3 for a hat and on bottom 1/3 for a beard, one cookie at a time. Sprinkle red sugar for a hat and coconut on beard. Press on a marshmallow for tassel of hat, raisins for eyes, and a cinnamon candy for nose.