Heat grill. In large bowl, combine corn, potatoes, carrots, zucchini and onion. In small bowl, combine all remaining ingredients; mix well. Pour butter mixture over vegetables; toss to coat. Cut four 18x12-inch pieces of heavy-duty foil. Wrap each packet securely using double-fold seals, allowing room for heat expansion.
When ready to grill, place packets, seam side up, on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 25 to 35 minutes or until vegetables are tender.
To serve, open packets carefully to allow steam to escape.