Preheat oven to 400°F.
Wrap each color beet separately in foil and bake for 1 hour and 15 minutes until soft. Remove from foil, run under cold water and then remove peels. Cut each beet into quarters or eighths and place each color in its own bowl. Sprinkle with salt and pepper. (Note: The beets can be prepared up to two days in advance and kept in the refrigerator, covered tightly.)
Cut all peels and pith off oranges, working over a bowl to catch the juice for dressing. Cut between membranes, releasing segments.
Peel and clean fennel. Using a peeler, peel crosswise to create paper-thin strips.
When ready to serve, mix together beets, oranges and fennel. Top with mint and toasted hazelnuts. Mix ingredients for dressing and drizzle over salad. Serve at room temperature.
You can use all red beets if golden beets are not available.
DAIRY OPTION: Add feta cheese before serving.