1. In a large bowl, combine 2 quarts of the water with the vinegar. Peel the salsify under cool running water. Cut the roots into 4-inch lengths, adding them to the vinegar water as you work. Drain the salsify, transfer to a medium saucepan and add 2 quarts of fresh water and a generous pinch of salt. Bring to a boil and cook over moderately high heat until tender, 8 to 10 minutes.
2. Drain the salsify, reserving 3 tablespoons of the cooking water. In a food processor, combine the salsify and the reserved cooking water with the cream, butter and horseradish and puree until smooth. Season with salt and white pepper. Work the puree through a fine sieve and serve hot, sprinkled with parsley.
Make Ahead: The puree can be refrigerated for up to 1 day.