Heat oven to 350°F (325°F for dark or nonstick pan). Spray bottom only of 13x9-inch pan with baking spray with flour.
In medium bowl, toss carrots and raisins with 1/3 cup cake mix to coat. In large bowl, beat remaining cake mix, cinnamon, water, egg product, applesauce and oil with electric mixer on low speed 30 seconds, then on medium speed 2 minutes, scraping bowl occasionally. Stir in carrot mixture until blended. Pour batter into pan; spread evenly.
Bake 33 to 38 minutes or until center of cake feels firm or toothpick inserted in center comes out clean. Cool cake in pan on cooling rack at least 1 hour.
Reserve 1/2 cup of the frosting. Spread remaining frosting over top of cake. Spoon 1/4 cup of the reserved frosting into small resealable freezer plastic bag; spoon remaining frosting into second bag. Add red and yellow food colors to one bag; add green food color to other bag. Seal bags; squeeze bags to tint frosting evenly.
Pull tip of knife through frosting on top of the cake to score 16 serving pieces (4 rows by 4 rows). Cut 1/8-inch tip off 1 bottom corner of bag with orange frosting. Diagonally on each scored cake piece, pipe a carrot by squeezing frosting in a thick line, letting up on pressure at end to draw to a point. Cut off tiny corner of bag with green frosting. At top of each carrot, pipe loops of green frosting for carrot tops. Refrigerate until frosting is firm before serving, about 30 minutes. Store loosely covered in refrigerator.