Combine water, apple, and cranberries together in a bowl; bring to a boil. Cook mixture until cranberries burst and apple is tender, about 5 minutes. Reduce heat to medium and stir oats, brown sugar, cinnamon, nutmeg, and salt into apple mixture. Cook, stirring continuously, until water is absorbed and oatmeal thickens, 2 to 3 minutes. Top oatmeal with walnuts.
