Combine cabbage, carrots, and celery in a large bowl. Whisk vinegar sugar, salt, and pepper together in a small bowl; pour over cabbage and stir until well coated. Refrigerate cabbage mixture for 15 minutes.
Mix mayonnaise, horseradish, and mustard together in a bowl; stir into cabbage mixture. Add parsley, celery seed, onion powder, and mustard; mix well. Refrigerate until chilled, at least 30 minutes.