In a large saucepan, cook the turnips and parsnips in lightly salted boiling water for 5 minutes. Add the potatoes and cook for another 8 to 10 minutes or until vegetables are just tender. While the vegetables are cooking, heat the cream, butter and horseradish in a small saucepan over low heat (do not simmer or boil). Drain vegetables and put them back in the large saucepan and cook over moderately high heat stirring constantly to evaporate excess moisture. Remove from heat. Strain the cream mixture into vegetables pressing down on solids to extract as much of the flavored cream as possible. Mash vegetable by hand leaving them a little chunky. Stir in parsley, cheese if using, and season to taste with salt and pepper. Serve immediately.