Place the potatoes in a medium pot. Add enough cold water to cover the potatoes by 2 inches. Place the pot over high heat and add 1 teaspoon salt. Bring the water to a boil and cook the potatoes, covered until tender, 20 to 25 minutes.
Just before the potatoes are cooked, combine the half-and-half, butter, and horseradish in a medium microwave-safe bowl. Microwave on low for 1 to 2 minutes, until the butter is melted.
Drain the potatoes and transfer to a medium mixing bowl. Use a potatoes masher or large fork to smash the slightly. Pour in the half-and-half mixture and continue to mix until the potatoes are smashed, leaving some lumps. Season with salt and pepper to taste. Serve immediately.