Combine the sugar or sugar substitute, salt, pepper, horseradish, onion, celery seed, cream, mayonnaise, vinegar, and lemon juice in a small bowl. Whisk until well blended and smooth.
Chop cabbage fine. This can be done in the food processor.
Put chunks of cabbage in the bowl of the food processor and pulse until the cabbage is chopped fine. You will need to do this in batches.
Add chopped cabbage to the large bowl with diced onions and grated carrots.
Stir in the dressing.
Cover and refrigerate for at least two hours before serving.
Notes
Note: nutrition values are an estimate only and may vary depending on your exact ingredients and quantities used.