Combine apples, cranberries, water, and sugar in a Dutch oven. Bring to boiling; reduce heat. Cover and simmer for 8 to 10 minutes or until apples are tender and most of the skins of the cranberries have popped, stirring the mixture occasionally.
If necessary, slightly mash mixture with a potato masher to desired texture. Stir in the peel. Serve warm or chilled. Makes 8 servings (about 4 cups).