In a large mixing bowl combine apples and sugar. Gently fold in cranberries, carrots and nuts. In another bowl combine flour, baking powder, baking soda, salt and cinnamon. Mix well. Add to apple mixture. Mix well to moisten dry ingredients. Combine eggs and oil; stir into apple mixture. Fill 18 greased muffin tins 2/3 full.
Bake at 375 degrees for 20-25 minutes. Cool 5 minutes before removing from tins.