Place the oven rack in the middle position. Preheat the oven to 350 degrees F. Grease a 10" spring-form cake pan with vegetable oil spray.
Combine the sugar, applesauce, eggs and vanilla in a bowl. Place flour, baking soda, baking powder, salt, cinnamon and nutmeg in a second bowl and whisk to combine. Mix the dry mixture into the wet. Stir in carrots, pineapple, walnuts and cranberries. Spoon the batter into the pan. Bake 45 to 50 minutes, or until the cake springs back when gently touched in the very centre. Cool to room temperature, dust with icing sugar, cut into wedges and serve.