1. Preheat oven to 350°.
2. Weigh or lightly spoon flours into dry measuring cups; level with a knife. Combine flours, xanthan gum, and next 5 ingredients (through nutmeg) in a medium bowl; stir with a whisk.
3. Place buttery spread and sugars in a medium bowl; beat with a mixer at medium speed until light and fluffy. Add eggs, 1 at a time, beating well after each addition. Beat in applesauce. Add flour mixture; beat at low speed just until combined. Stir in carrot, coconut, and raisins.
4. Place 16 paper muffin cup liners in muffin cups; coat liners with cooking spray. Spoon batter into prepared cups, and sprinkle with walnuts. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan on a wire rack; remove from pan.