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