Heat oven to 350°F. Line 13x9-inch pan with foil so edges extend over 2 sides of pan. Cut cookie dough into 4 pieces. In pan, press dough evenly in bottom. Bake 15 to 20 minutes or until edges are golden brown. Cool completely in pan, about 20 minutes.
Use foil to lift cookie from pan; carefully remove foil. Place cooled cookie on large serving platter or foil-covered 14x10-inch sheet of cardboard. To create puzzle, use cookie cutters to cut a variety of shapes in baked cookie. Carefully remove shapes from background.
Divide frosting into several small microwavable bowls. Tint frostings as desired with food color. Microwave 1 bowl of frosting at a time for 10 seconds; stir until smooth.
Carefully frost and decorate cut shapes and background as desired. Let stand until set. Return shapes to puzzle.