Bring 1 cup of the milk to boil in medium saucepan. Stir in rice, apple, raisins, cinnamon and nutmeg; cover. Remove from heat. Let stand 5 minutes.
Meanwhile, prepare pudding in large bowl as directed on package with remaining 2 cups milk.
Stir rice mixture into prepared pudding. Stir in walnuts. Cover surface of pudding with plastic wrap; cool 5 minutes. Serve warm or chilled