Peel off the outer leaves of the napa cabbage and radicchio, cut out the core, and julienne.
Combine the cabbage, radicchio, carrots, vinegar, and salt in a large bowl and toss thoroughly to combine. Add the mayonnaise, horseradish, sugar, and celery seed. Mix until all of the ingredients are thoroughly combined, and adjust salt to taste. Serve immediately, or chill in the refrigerator