In a large saucepan combine the beets and enough water to cover them by 1", bring to a boil, and simmer the beets, covered, for 20 to 40 minutes( depending on their size), or until they are very tender.Drain the beets, reserving 1 tbsp. of the cooking liquid, and slip off the skins and stems. In a food processor puree the beets with the reserved cooking liquid, the horseradish, the vinegar, and salt and pepper to taste. The puree may be made up to 1 day in advance and kept covered and chilled. In a heavy saucepan reheat the puree over low heat, stirring constantly, until it is hot. Makes about 3 cups.