Preheat oven to 350 degrees. Wrap foil around garlic bulb and place in heated oven for 45 minutes. Meanwhile place turnips in a pot of cold salted water and bring to simmer. Cook turnips until soft.. about 15 20 minutes. Drain turnips very well and let dry for a few minutes.
Using a potato masher, mash turnips, garlic. Stir in chilled butter, horseradish, salt, pepper and nutmeg and mix well. If needed add heated cream. Stir in chives just before serving.