Preheat oven to 400ºF. Scrub beets and wrap them in foil. Set them on a roasting pan and bake them for 1 hour. When cool enough to handle, (15 min or so) rub off the skins using a paper towel, or use a vegetable peeler. Cut them into 1/2-inch dice.
While beets are baking put potatoes in a large pot and cover with cold water by a few inches. Add a teaspoon of salt. Bring to a boil over high heat. Lower to a gentle simmer. Simmer for 20 minutes and check for doneness. Potatoes are done when tender all the way through. Test with a fork or skewer. Drain and cool. Cut into 1/2-inch dice.
In a small bowl combine the dressing ingredients: mayonnaise, yogurt, mustard, horseradish, 1 teaspoon of salt, and pepper.
In a large bowl toss all the chopped ingredients with the dressing. Chill for at least an hour.
Garnish with sliced eggs and parsley, if you like.