Cover potatoes with 2 inches of salted cold water in a 5-quart heavy pot, then simmer, uncovered, until very tender, about 25 minutes.
While potatoes are simmering, bring half-and· half, butter, salt, and pepper just to a simmer, stirring until butter is melted. Keep hot, covered.
Drain potatoes in a colander, then immediately force through ricer into a large bowl.
Stir in hot milk mixture, then horseradish.