Preheat the oven to 400 degrees F. Cut each sheet of puff pastry into four squares. Place equal amounts of cherry pie filling in the center of each square. Brush the edges with water and fold in half diagonally. Seal and crimp the edges with a fork. Bake on ungreased baking sheets for 15 to 18 minutes, or until puffed and golden. Meanwhile, in a small bowl, combine the confectioners' sugar and water; mix well. Drizzle over the warm turnovers and serve.