Beat butter and shortening at medium speed with an electric mixer until blended. Add powdered sugar, egg, and vanilla to butter mixture; beat well. Gradually add flour, cream of tartar, and baking soda, beating well.
Cover and chill dough 1 hour. Roll dough to 1/4-inch thickness, and cut with a 4-inch ghost-shaped cutter. Place cookies 2 inches apart on lightly greased baking sheets. Place a craft stick under each cookie, pressing cookie lightly onto stick.
Bake at 375° for 10 minutes or until cookies are lightly browned. Cool cookies on baking sheets 5 minutes; remove to wire racks to cool completely.
Microwave frosting in a 2-quart glass bowl at HIGH 1 minute or until frosting melts. Spread melted frosting over cookies in batches of 3. (Frosting hardens quickly.) Decorate rapidly with desired toppings.