In large bowl, beat butter, powdered sugar, egg and orange peel with electric mixer on medium speed, or mix with spoon. Stir in flour, baking soda and cream of tartar.
Divide dough into thirds. Tint one portion red and one portion green; leave remaining portion plain. Flatten each portion into a disk. Wrap in plastic wrap; refrigerate 20 minutes.
On separate sheets of lightly floured waxed paper, roll each portion of dough into 12x9 inch rectangle. Place red rectangle on top of green re tangle, using waxed paper ends to help flip dough over. Top with plain dough rectangle. Starting on a long side, and using waxed paper as an aid, roll dough into a cylinder. Wrap into plastic; refrigerate 1 hour.
Heat oven to 375 degrees F Cut dough into 1/4 in slices. On ungreased cookie sheet, place slices about 1 inch apart. Sprinkle with coarse sugar.
Bake 7 to 8 minutes or until edges are set. Cool 1 minute; remove from cookie sheet to cooling rack.