Scrub the new potatoes with a stiff brush, leaving peel on the potatoes, if you like. Cut them into halves or quarters. In a large saucepan, cook the potatoes in a small amount of boiling, lightly salted water for 15 to 20 minutes or till tender. Drain off water.
Mash with a potato masher or beat with an electric mixer on low speed. Add butter and horseradish. Season to taste with salt and pepper. Gradually beat in cream or milk to make light and fluffy. Makes 8 servings.