For the Sugar Cookies, mix flour, cream of tartar, baking soda and salt in medium bowl. Set aside.
Beat granulated sugar and butter in large bowl with electric mixer on medium speed until light and fluffy. Add eggs and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Refrigerate 2 hours or until firm.
Meanwhile, for the Colored Sugar, place sugar in resealable plastic bag. Add 5 drops of desired food colors. Add more food color, a drop or two at a time, if more intense color is desired. Seal bag and knead gently until color is evenly distributed. Spread in thin layer on baking sheet and break up any large lumps. Allow to dry thoroughly, about 15 to 20 minutes. Sift or press through sieve to return sugar to its original texture, if needed. Set aside.
Preheat oven to 400°F. Shape dough into 1-inch balls. Roll in Colored Sugar. Place 2 inches apart on ungreased baking sheets.
Bake 6 to 8 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.