Cook beets, remove skins, and cut into ½-inch dice. Peel potatoes and carrots and cook until each vegetable is tender but not mushy (about 20 minutes for potatoes and 10 minutes for carrots). When cool, cut into ½-inch dice. In a large bowl combine beets, potatoes, carrots, pickles, scallions, and dill. Toss vegetables gently, season with salt and pepper, and add hard-boiled eggs. Cover and refrigerate to chill thoroughly before serving.

For dressing: Combine yogurt, mayonnaise, horseradish, lemon juice, and sugar in a blender, and mix until smooth. Season to taste with pepper. Pour dressing over the vegetables and chill until served.