Freeze cookie dough at least 1 hour.
Heat oven to 350degreesF. Cut chilled dough into 1/4-inch slices. (Return dough to freezer if it becomes too soft to cut.) On ungreased cookie sheet, place slices 3 inches apart.
Bake 8 to 12 minutes or until golden brown. Cool 2 minutes; remove from cookie sheets to cooling racks. Cool completely, about 5 minutes.
In small bowl, beat powdered sugar, butter and enough milk until smooth and desired spreading consistency. In small bowl, place half of frosting. Add red food color; stir until blended.
Frost cooled cookies with red and white frosting. Use small amount of frosting to attach chocolate chips for eyes and cinnamon candy for nose. Gently press coconut into white frosting for beard. Press marshmallow into red frosting for tassel on cap. Let stand until frosting is set. Store between sheets of waxed paper in tightly covered container.