Disney has really been working on improving their food offerings to include more healthful choices, and I think you'll be very pleased with the choices. At each park, you will find "fruit stands" that offer a variety of fresh fruits, vegetables, and other snacks such as nuts. In fact, this is often where we eat for breakfast! For your youngest, there are soft fruits such as bananas, strawberries, and watermelon cubes. I've also seen yogurt available.
At the ice cream carts, not only is there the usual sweet treat, but there are frozen fruit bars that are basically just that, fruit! A very popular spot at the Magic Kingdom is Aloha Isle that sells a variety of sweets made from pineapple juice and even has pineapple spears available.
While dining, the sides that are offered with kids' meals are applesauce, carrots, and grapes; but french fries are still available if you'd like to cheat a little bit! And instead of soda being the drink, kids can get different milks and juices.
You'll even notice at the stores that sell pre-packaged snacks that while there are still plenty of sweets to satisfy the occasional junk food craving, there are many bags of dried fruits/nuts, pretzels, and little cheesy crackers (like Goldfish) that I think are nice for toddlers.