Hi Sheri! I have good news for you straight from the chefs at the Port Orleans -- the beignets are safe for those with peanut and tree nut allergies! (Of course, as ingredients are always subject to change, you should verify this information again prior to ordering a beignet.)
You'll also be able to find ice cream that does not contain nuts throughout the Disney parks and resorts. However, even though many varieties of ice cream do not contain nuts, they are made in a facility that also processes nuts. When your son wants ice cream, the restaurant or quick-service location can provide you with a list of ingredients and more information so you can make an informed decision.
Also, if you're planning to visit the Animal Kingdom, you should know that the animal keepers have nuts in their pockets to use with the birds throughout the park, and these keepers may have nut oil or remnants on their hands and clothing.
Did you know that Walt Disney World has a
Special Diets department to assist guests with food allergies? If you email
SpecialDiets@DisneyWorld.com in advance of your trip, they will send you a form to complete about your son's allergy and the restaurants in which you plan to dine. They will then make sure that each table-service restaurant has the information about your son's nut allergy so that they can prepare a nut-free meal for him. Also, when you arrive at each restaurant, ask to speak with a chef who can tell you which items on the menu or buffet are nut-free. The Special Diets department can also provide you with ingredient information for the foods at the various restaurants. (They were very helpful to me in obtaining the answer about the beignets!)
Come visit us again at the Moms Panel if you have more questions!