Cover potatoes with water in a saucepan; bring to a boil, reduce heat and cook just until tender. Drain potatoes. Bring a large pot of water to a boil. Add green beans and carrots. Cook just until tender; drain and immediately plunge into ice water. Drain well.
Combine all dressing ingredients in a bowl. Place potatoes, green beans, carrots, zucchini, onion and mushrooms in a large bowl. Add dressing and gently toss to mix.
Cover; chill 2 hours or overnight.