In large bowl, break up cookie dough. Stir or knead in flour until well blended. Reshape into log. If too soft to cut into slices, refrigerate up to 30 minutes.
Heat oven to 350°F. Cut dough into 34 (1/4-inch) slices. On ungreased cookie sheets, 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 spreadable. 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.