In large bowl, break up cookie dough. Stir or knead in flour until well blended. Reshape into log. Cut cookie dough lengthwise into 3 long slices (see diagram). On work surface, separate slices with rounded sides down. Lightly brush all cut surfaces with beaten egg white.
Sprinkle egg white area of 1 rounded slice with red sugar. Place middle slice on top; sprinkle with green sugar. Place remaining rounded slice, egg white side down, on top; press firmly and if necessary, reshape into roll. Wrap roll in plastic wrap; freeze 30 minutes.
Heat oven to 350°F. Cut roll into 24 slices; place 1 inch apart on ungreased cookie sheets.
Bake 9 to 11 minutes or until edges are light golden brown. Immediately press gumdrop half onto outer edge of each cookie to look like ornament hanger; remove from cookie sheets to cooling racks.