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. Serve immediately.