In medium bow; beat eggs, sugar and vanilla together until well mixed. Add yogurt and oil. Beat well. In a small bowl; stir together flour, baking soda and cinnamon. Add to egg mixture, stirring until smooth. Add carrots and apple and then nuts. Stir just until combined.
Spoon batter into well greased muffin cups almost to the top.
Bake in preheated 375°F oven for 20 to 25 minutes or until a toothpick inserted in middle of muffin comes out clean.