Leave roots and 1 inch stems on beets; scrub with a brush. Place in a medium saucepan; cover with water. Bring to a boil; cover, reduce heat, and simmer 15 minutes or until tender. Drain and rinse with cold water. Drain; cool. Trim off beet roots; rub off skins. Cut into quarters.
Steam peas, asparagus, and squash, covered, 3 minutes or until crisp-tender. Combine beets, peas, asparagus, squash, and remaining ingredients in a large bowl.