Preheat oven to 400. Stab a whole clove into each sweet potato and apple. Place into a roasting pan. Bake until the apples are soft, about 35 minute. (Don’t worry if some break or collapse.) Remove apples from the pan, and, if necessary, continue baking the sweet potatoes until very soft. Remove the pan and raise the oven temperature to 425 degrees.
Lightly oil a 2 quart baking dish. When cool enough to handle, remove the apple peels and skins and sweet potato skins. Press apples and sweet potatoes through the medium disk of a food mill or through a coarse sieve into a bowl. Stir in butter, salt, pepper and horseradish. Spoon into the baking dish.
Bake in the upper rack of an oven until slightly browned and bubbling at the edges, 15-20 minutes.
