Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in 1/4 cup flour until well blended. Remove half the dough, and refrigerate remaining dough until needed. In small bowl, mix 1/3 cup powdered sugar and 1 tablespoon flour.
Sprinkle half of sugar mixture onto work surface. With rolling pin, roll dough 1/8 inch thick. With 2-inch heart-shaped cookie cutter dipped in sugar mixture, cut out dough hearts. On ungreased cookie sheets, place hearts 2 inches apart. Repeat with remaining dough and sugar mixture.
Bake 7 to 9 minutes or until light golden brown. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 15 minutes.
In medium bowl, beat all frosting ingredients except food color until smooth and spreadable. Beat in desired amount of food color. Pipe or spread on cooled cookies. Let stand until frosting is dry. Store cookies in single layer in covered container.