Heat oven to 350°F. Coat two 8- or 9-in. round cake pans with nonstick spray.
Cake:Put first 5 ingredients in a large bowl; stir to blend. Make a well in center; add oil and eggs. Stir with rubber spatula, scraping down sides of bowl occasionally, until well blended. Stir in remaining ingredients. Divide between pans; spread evenly.
Bake 35 to 40 minutes until a wooden pick inserted in centers comes out clean. Cool in pans on a wire rack 10 minutes. Run a knife around cakes, then invert on rack to cool.
Meanwhile make Frosting: Beat first 3 ingredients in a large bowl with mixer on medium speed until blended. Reduce speed to low; beat in sugar. Remove 1⁄4 cup to a cup. Spoon 2 tsp removed frosting into another cup; tint green and scrape into a small ziptop bag. Using red and yellow food color, tint remaining frosting in cup orange. Scrape into another ziptop bag. Seal bags; refrigerate until needed.
To frost: Place 1 cake layer, top side up, on serving plate. Spread top with 1⁄2 cup frosting. Top with second layer, bottom side up. Spread remaining frosting over top and sides. Pat sides with chopped nuts.
To decorate:Lightly score the frosting into 12 wedges to use as a guide when piping the carrots. Briefly warm bags of frosting between hands. Use orange frosting to pipe 12 carrots on cake. Snip a tiny upside-down V in bottom corner of bag with green frosting; pipe carrot tops.