Fill a large kettle with cold water, lightly salted. Add peeled and chopped potatoes. Place on the stovetop over medium heat. Cook the potatoes until fork tender, approximately 20 minutes.
Heat milk and butter in a small sauté pan over low heat. Drain hot potatoes and return to the hot kettle (this will help evaporate excessive moisture). Using a potato ricer, rice the potatoes in the kettle. Slowly add the warmed milk/butter and horseradish, folding into potatoes with a large spoon. Add a little bit more milk or butter if the potatoes seem a little dry. Season with salt and pepper. Keep warm on a low burner on the stovetop or in a 150 degree oven. Garnish with chopped chives or scallions.