Cut first 4 ingredients into 1-inch cubes. Line 2 (13- x 9-inch) baking pans with aluminum foil.
Toss together onions, beets, 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper in one lined pan, and set aside.
Toss together parsnips, squash, remaining 2 tablespoons oil, remaining 1/2 teaspoon salt, remaining 1/4 teaspoon pepper, and maple syrup in empty lined pan.
Bake both pans at 350 for 45 minutes or until vegetables are tender, shielding with aluminum foil, if necessary, to avoid excessive browning.
Combine all baked vegetables.
Add salad greens, and toss. Arrange on a serving platter, and sprinkle with walnuts.