Hold each squash slice by an end; shave into ribbons with a vegetable peeler to measure 4 1/2 cups.
Repeat procedure with celery root, shaving to measure 1 1/2 cups.
Repeat procedure with apple, shaving to measure 1 cup.
Repeat procedure with carrot, shaving to measure 1/2 cup.
Combine vegetable ribbons in a large bowl; add 1/4 teaspoon salt, tossing to combine.
Combine remaining 1/4 teaspoon salt, vinegar, cider, and honey, stirring with a whisk.
Gradually add grapeseed oil, stirring constantly with a whisk.
Add vinegar mixture to squash mixture, tossing gently to coat.
Let stand 30 minutes. Add arugula just before serving, tossing to combine.
Sprinkle with pepper.