Combine barley and water in a small saucepan and bring to a boil. Reduce heat; cover and simmer for about 30 minutes or until barley is tender. Drain and rinse with cold water; drain well.

Meanwhile, in a large bowl, combine beets with vinegar, mint, salt and pepper. Stir in cucumber, carrots, onion and cooked barley. Add feta cheese to serve (optional).