Beat first 4 ingredients in large bowl with mixer until blended. Add flour and baking soda; mix well. Refrigerate 30 min.
Heat oven to 375ºF. Roll dough to 1/8-inch thickness on floured surface. Cut into shapes with 3-inch cutters. Place on baking sheets sprayed with cooking spray.
Bake 10 min. or until edges are lightly browned. Cool 3 min.; remove to wire racks. Cool completely.
Meanwhile, beat powdered sugar, milk and corn syrup until blended. Spoon 3/4 of the icing into resealable plastic bag; seal bag. Spoon remaining icing into 2 resealable plastic bags; tint icing in one bag with 1/4 tsp. red food coloring, then tint remaining icing with 1/4 tsp. green food coloring.
Snip small corner from bottom of each bag. Pipe plain icing onto cookies, then pipe red and green icings into stripes on cookies. Swirl with toothpick.