Steam raw beets in water in saucepan until tender. Slip off skins. Rinse to cool. Slice in 1/2-inch rounds. In a medium bowl, toss with red wine vinegar.
In a large bowl, combine balsamic vinegar, olive oil and water. Add salad greens and toss.
Put greens onto individual salad plates. Top with sliced beets, and chopped apples and celery. Sprinkle with pepper, walnuts and cheese. Serve immediately.