Sift together flour, cream of tarter, baking soda, nutmeg, and cinnamon in a bowl; set aside. Beat the butter and sugar with an electric mixer in a large bowl until smooth. Add the eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Beat in the vanilla with the last egg. Mix in the flour mixture until just incorporated. Cover and refrigerate dough overnight.
Preheat an oven to 350 degrees F (175 degrees C). Roll out dough on floured surface to 1/2 inch thick. Cut into shapes with Christmas cookie cutters. Place cookies 1 inch apart on ungreased cookie sheets.
Bake in the preheated oven until the edges are golden, 8 to 10 minutes. If using cutters that have small appendages, such as reindeer legs, reduce the baking time or they will overcook. Remove cookies to a wire rack to cool completely.
Beat the butter and confectioners' sugar with an electric mixer in a large bowl, mixture will be stiff. Add the vanilla and slowly mix in the milk a little at a time until a spreading consistency is reached. Stir in food coloring, if desired. Make sure cookies are completely cool before frosting.
