Place the potatoes and carrots in a pot and cover them with cold salted water by a few inches (8 cm). Bring to a boil and cook until the potatoes are tender, 10-15 minutes. Drain and cool.
In a large bowl, combine the mayonnaise, yogurt, mustard, vinegar, horseradish, pickle, dill and onion. Add the potatoes and carrots and toss well. Serve immediately or chill for up to 1 day. Serves 4.