In a large bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. Divide dough into thirds. Cover and chill dough for 1 to 2 hours or until dough is easy to handle.
Preheat oven to 350 degrees F. On a 15x10-inch piece of parchment paper, roll one dough portion into an 8 1/4- to 8 3/8-inch circle. Place an 8-inch round baking pan on top of dough circle. Using a sharp knife or pastry wheel, cut around pan, evenly trimming away extra dough. Transfer parchment paper holding dough circle to a cookie sheet.
Bake in the preheated oven for 5 minutes. Remove cookie sheet from oven. Using the desired shapes of decorative cookie cutters, cut into dough, but do not remove shapes. Bake in the preheated oven for 4 to 6 minutes more or until edges are firm and very light brown. Remove from oven.
Using the same cookie cutters, recut shapes in the dough circle but do not remove shapes. Slide parchment with the circle to a wire rack; cool completely. Carefully remove cutouts from the circle by lightly pressing up from the bottom. Set aside cutouts. Repeat rolling and baking the remaining two dough portions.
Divide Creamy White Frosting into desired number of individual bowls. Using assorted paste food colors, tint each portion of the frosting with the desired color.
Frost the remainder of the circle to resemble a snow globe. (For sky, frost the top half of the circle with light blue frosting. For snow, frost the bottom half of the circle with untinted frosting.) Frost each cutout cookie as desired. If desired, add decorative sprinkles, edible glitter, chocolate-caramel logs and/or candies. Let stand until frosting sets.
Place each cutout cookie into its original spot in snow globe cookie.
Creamy White Frosting
In a large mixing bowl beat butter with an electric mixer on medium to high speed until smooth. Gradually add 1-1/2 cups of the powdered sugar, beating well. Beat in 1/4 cup milk and the vanilla until combined. Gradually beat in the remaining powdered sugar and enough additional milk (1 to 2 tablespoons) to reach spreading consistency.