Peel and quarter the potatoes and cover with cold water. You can hold the potatoes this way at room temperature for 6 hours ahead of cooking (or for a day ahead in the refrigerator).
Drain the potatoes, put them in a 6-qt. pot, and cover with water. Add 1 Tbs. salt. Bring to boil, reduce to a gentle boil, and cook until fork-tender, 25 to 30 minutes. Pour off the water and let the potatoes cool. (If they sit in water off the heat, they'll turn pasty.)
In an electric mixer with the whisk attachment, whip the potatoes until smooth, about 1 min.; add the butter and mix until melted and combined, about 30 seconds. Add the cream, 2 Tbs. salt, and pepper; whip until smooth and creamy, about 2 min., scraping down the sides of the bowl frequently. (You can also use a food mill.) Fold in the horseradish and combine well.
To keep the potatoes warm -- Put an inch of water in the pot the potatoes were cooked in and set over low heat. Put the potatoes in a mixing bowl, cover with foil, and put the bowl on top of the pot. You can hold the potatoes like this for at least 2 hours; just maintain the water level and keep the heat low.