Soak wood chips in water 30 minutes. Drain well.
Place wood chips on hot coals. Place a mesh rack on a grill rack over hot coals. Place mussels on mesh rack; cover and cook 3 minutes or until shells open. Remove from heat, and discard any unopened shells. Cool mussels. Remove meat from shells; discard shells.
Combine vinegar, oil, and mustard in a large bowl, stirring with a whisk. Add mussels, greens, and remaining ingredients; toss gently to coat.