Put the unpeeled whole potatoes in a large pot with cold water to cover by about 2 inches. Bring to a simmer, and cook until tender, about 30 to 40 minutes. Drain, and let sit until just cool enough to peel.

While the potatoes cool, combine the butter, half-and-half, milk, and salt in the cooking pot over low heat, just until the butter melts.

Use a ricer, and press the still-warm potatoes through into the butter mixture. Add the horseradish, and stir until smooth. Adjust seasoning, and serve immediately.

*The ½ cup of grated fresh horseradish called for here will give the mashed potatoes a moderate heat; for a more intense flavor, add up to 1 cup. Fresh horseradish is best, but if it is unavailable, use about ½ cup jarred horseradish. Drain the liquid from the jarred horseradish, then rinse, pat it dry with a paper towel, and proceed to use as fresh.