In large bowl with electric mixer, beat granulated sugar, powdered sugar and butter on medium speed until light and fluffy. Beat in oil, vanilla and eggs until well blended.
On low speed, beat in flour, baking soda, cream of tartar and salt until a dough forms. Cover with plastic wrap; refrigerate at least 2 hours or overnight for easier handling.
Heat oven to 375°F. Shape dough into 1-inch balls; place 2 inches apart on ungreased cookie sheets. Flatten each with bottom of glass dipped in colored sugar.
Bake 5 to 8 minutes or until set but not brown. Immediately remove from cookie sheets.