Place the potatoes in a large pot with enough water to cover. Bring to a boil, and cook for about 10 minutes, or until tender. Drain, and place in a serving bowl.
Stir the onion, salt and pepper into the potatoes while they are still hot. This allows the potatoes to absorb the flavor. Allow to cool for about 20 minutes.
Add the mayonnaise, mustard and horseradish to the salad, and mix well. Gently stir in the eggs and dill pickles. Finish off with a generous grinding of black pepper on top. Chill for about 30 minutes before serving.