Place the potatoes in a 5-quart saucepan and cover with water. Add a large pinch of kosher salt, about 1/2 teaspoon. Bring to boil over high heat, then simmer until potatoes are tender to the tip of a knife. Drain and potatoes and place into a bowl. Add the buttermilk and cream cheese and mash until smooth. Fold in the chives and the horseradish.