Using a rolling pin, roll the refrigerated dough (or your cookie dough from scratch) to about 1/4-inch thick. With a cookie cutter, cut into circles.
Arrange dough in a single layer on a baking sheet and bake in the oven according to recipe or package directions. Allow to cool completely.
Sprinkle some cornstarch on a clean working surface, as well as on the rolling pin. Roll out the fondant to about ¼-inch thick.
Using the same size cutter for the cookies, cut out 6 fondant circles.
Cut each circle in half and press the demi-circles fondant onto the cookies to resemble Santa’s hat.
In a bowl, combine, butter, sugar, and milk. Beat at medium speed, gradually increasing to high until smooth and form stiff peaks.
In a piping bag fitted with a star tip, spoon in buttercream frosting.
On each cookie, pipe a border around the edge of the fondant to resemble “fur”. Pipe a small dollop on the top of fondant to resemble a pompom.
Pipe on the lower edge of the cookies to make a beard.
Using the red decorating frosting, pipe a small dollop to resemble a face.
Using the black frosting, dot two eyes between the beard and the hat.