Cook the potatoes in boiling salted water about 20 minutes, until tender. Drain, then return to the pot.
Combine the milk and garlic in a large saucepan over medium-heat and bring to a boil. Pour the milk mixture over the potatoes and add the horseradish. Use a potato masher to mash until smooth. Stir in the butter until melted, and season to taste with salt and pepper. Serve hot.