Roll out dough to 1/4-inch thickness; cut with a 2-inch star-shaped cookie cutter. Place on baking sheet, and insert a short wooden skewer halfway into side of each cookie. Bake as directed.
Meanwhile, combine powdered sugar, half-and-half, and vanilla, stirring with a whisk until icing is smooth. Divide into batches, and tint with desired amount of red or blue food coloring. Spoon icing onto cooled cookies, and spread to edges.