Bake beets, covered with foil, at 400° for 30 minutes or until tender. Cool, remove skins, and cut into thin wedges.
Cook corn in boiling water to cover until crisp-tender, and drain. Plunge into ice water to stop the cooking process; drain. Repeat with green beans and peas.
Toss spinach and lettuce with 1/4 cup Shallot Vinaigrette in a large bowl. Cut corn kernels from cobs, and combine with beets, beans, peas, and red onion. Top greens with beet mixture, walnuts, and goat cheese. Drizzle with dressing to taste.