Put the milk, butter, nutmeg and some black pepper into a pan and put it over low heat to melt the butter.  Grate the horseradish root into the hot milk and butter mixture, and then leave to infuse for a half an hour (off the heat).  Add a tablespoon of salt to a large pan of water and bring to a boil. Cut the potatoes into roughly equal pieces.  Pour cold water over them, stir briefly, and then drain. Add the potatoes to the pan when the water is boiling.  Turn down the heat to a simmer and cook until the potatoes are easily pierced with a fork.  Pour into a colander and leave for at least 3 minutes (this lowers the water content in the potatoes).   Warm your milk and butter mixture until hot, but not quite boiling.   Pile the potatoes into a potato ricer or food mill and squeeze them into the seasoned hot milk.    Stir well with a wooden spoon to get a smooth, even texture, then taste for seasoning.  Serve at once.