In a large bowl, beat butter, granulated sugar, and brown sugar with a mixer on medium speed until fluffy, about 3 minutes. Beat in egg and vanilla. With mixer on low speed, fold in flour until just blended. Shape dough into two 1-inch-thick disks; wrap in plastic and refrigerate 1 hour.

Heat oven to 350 degrees F. On a floured surface, roll each disk to a 1/4-inch thickness. Use 3-1/2-inch ice-skate and mitten cookie cutters (you can buy them at sugarcraft.com) to cut out 12 of each shape. Transfer cookies to ungreased baking sheets. Bake 12 minutes, or until golden. Let cool 3 minutes, then cool completely on a wire rack.

To decorate the ice-skate cookies, spread with thin white royal icing (see www.parents.com for recipe); let dry at least four hours. Cover and refrigerate excess icing until ready to use. Cut off part of the curves of 2 mini candy canes and use icing to attach as blades. Tint the remaining royal icing with red or blue food coloring until it's pink or blue, then transfer 1 cup to a pastry bag with a #2 tip (available in craft stores and some supermarkets). Pipe tinted frosting over the white icing to create laces and other details. Decorate with pink or blue sugar and jumbo rainbow nonpareils; let dry completely.

To decorate mitten cookies, spread thin blue or pink royal icing on mittens, and use a pastry bag with a #2 tip to pipe thick white royal icing on cuffs. Decorate with jumbo rainbow nonpareils, yellow sugar, diamond sprinkles, and coconut while icing is still wet. Let dry completely.