In a large pot, cover potatoes with water and season with salt. Bring to a boil and cook until potatoes can be easily pierced with a fork, 16 to 18 minutes. Drain and return to pot. Use a potato masher to mash potatoes until smooth.
Meanwhile, in a small saucepan over medium heat, melt butter with milk until warm. Pour mixture over potatoes and stir until creamy. Stir in sour cream and horseradish then season with salt and pepper. Transfer potatoes to a serving bowl and top with a pat of butter. Season with more pepper and garnish with chives before serving.
