Trim off leaves of broccoli; discard tough ends of lower stalks. Cut broccoli into bite-size pieces.
Combine broccoli, cauliflower, carrots, mushrooms, green peppers, celery, zucchini, and cucumber in a large serving bowl; mix well.
Combine vinegar, oil, sugar, mustard, garlic, salt, and tarragon; mix well. Pour over vegetables, and toss well. Cover and refrigerate overnight.