While there are certainly many offerings of all things sweet, salty, and fried, Disney has many, many offerings that are healthful throughout the parks and resorts. For example, the kids menus have sides that are usually a choice of vegetables or fruit with juice, milk (even soy!), and water as the beverage choices. French fries and soft drinks have to be requested. At the parks, there are fresh produce stands that sell a variety of fresh fruit and veggies. At little snack shops that do have the "goodies," you will also be able to find packaged variety of nut snacks and other similar choices.
Disney also does an incredible job meeting the diverse dietary demands of guests: sugar-free, vegan, vegetarian, gluten-free, allergies, etc. When making Advanced Dining Reservations, if you have any special dietary needs, you can just make a notation in your reservations. You can also talk to your server at any restaurant who can help you out, even providing you with an opportunity to speak to the chef or provide you with a list of ingredients.
I do want to mention a new restaurant:
Wave at the Contemporary Resort. Its focus is to offer healthful choices on the menu, so it may be a fun place to try out!