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Combine the ingredients for the dressing in a small mixing bowl, cover, and refrigerate.
Put the cabbage in a metal kitchen colander or spread it out on a rimmed baking sheet.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes).
Smoke the cabbage for 30 minutes. Transfer to a large mixing bowl.
Add the dressing and stir to coat the cabbage. Taste for seasoning, adding more sugar, horseradish, or salt and pepper as needed. Dust the top lightly with paprika. Refrigerate until serving time.