1Use sharp knife to cut cabbage head into quarters and remove core. Place 1 quarter, flat side down, on cutting board. Slice cabbage thinly with knife. Cut slices several times to make smaller pieces. Repeat with remaining quarters. You will need about 10 cups shredded cabbage.
2In large bowl, mix mayonnaise, horseradish, vinegar, mustard, sugar, salt, celery seed, pepper and garlic. Add carrots and cabbage. Stir well to combine. Serve immediately or refrigerate up to 3 hours.