Combine ingredients for horseradish sauce in small bowl and chill.
Combine ingredients for applesauce in a pot, bring to a boil, reduce heat to medium and cook until apples break down into a thick sauce, 20-25 minutes. Transfer to serving dish.
Grate potatoes and salt them, place in a strainer and drain 20-30 minutes. Press out all the excess liquid and add to a mixing bowl. Combine with parsnips, onion, egg, flour or matzo meal and pepper.
Heat a quarter inch of oil in a large skillet over medium to medium-high heat. Add potato mixture in 3- to 4-inch mounds, gently press down and cook 3-4 minutes on each side to deeply golden. Keep warm on a rack set over a baking sheet in warm 275ºF oven.
Serve potato pancakes with sauces alongside.