Cook wild rice according to package directions. Cool completely.
In a large bowl, combine sauerkraut, apple, celery, carrot, onion and cooled rice. In a small bowl, whisk the first five dressing ingredients until sugar is dissolved; stir in herbs. Add to sauerkraut mixture; toss to combine.
Refrigerate, covered, at least 4 hours to allow flavours to blend. Stir in walnuts just before serving.
Tip: To toast nuts, bake in a shallow pan in a 350° oven for 5-10 minutes or cook in a skillet over low heat until lightly browned, stirring occasionally.