Melt 1/4 cup butter in large skillet over medium heat. Add onions; saute until deep golden, about 30 minutes. Add vinegar and thyme. Reduce heat to low; saute 4 minutes. Season with salt and paper.
Meanwhile, cook potatoes in large pot of boiling salted water until very tender, about 20 minutes. Drain. Return to same pot; mash until smooth. Add 6 tablespoons milk, horseradish and 6 tablespoons butter; stir to blend. Thin with 2 tablespoons milk if necessary. Add 1 to 2 tablespoons more butter if necessary. Season with salt and pepper.
Transfer potatoes to serving dish. Spoon onion mixture atop potatoes. (Can be prepared 8 hours ahead. Cover with foil and refrigerate. Rewarm in 350ºF oven about 30 minutes). Serve hot.