1Scrub, top, and tail beets. Boil in salted water about 45 minutes, or until tender. Drain hot water from pot, and fill with cold water. Set aside until beets are cool enough to handle.
2Slice beets thinly, and transfer to a salad bowl. Add onion and cucumber.
3In separate bowl, combine yogurt, mayonnaise, vinegar, mustard, horseradish, dill, and salt and pepper. Pour over vegetables, and toss to combine. Refrigerate 2 hours, or overnight. Serve chilled.