Place potatoes in large saucepan with water to cover by 1 inch. Bring to boil over high heat, reduce heat to medium, and simmer until potatoes are just tender, about 20 to 30 minutes. Drain.
Set food mill or ricer over now-empty but still-warm saucepan. Spear potato with dinner fork, then peel off skin with paring knife; repeat with remaining potatoes. Working in batches, cut peeled potatoes into rough chunks and drop into food mill or ricer. Process or rice potatoes into saucepan or mash potatoes with potato masher directly in saucepan.
Stir butter into potatoes until just incorporated. Sprinkle salt and pepper over potatoes. Whisk horseradish into warm half-and-half; add mixture to potatoes and stir until just combined. Serve immediately. 4 servings.