Cook potatoes in large pot of boiling salted water until tender, about 20 minutes. Drain. Return to pot.
Meanwhile, bring 1 1/3 cups milk and garlic to boil in large saucepan. Add milk mixture and horseradish to potatoes. Using potato masher, mash until smooth. Add butter; stir until melted. Season with salt and pepper. (Can be made 2 hours ahead. Let stand at room temperature. Stir over medium heat until heated through, adding more milk to thin if necessary.).