In a large bowl, stir together the cream cheese and peppermint extract. Gradually add the powdered sugar, stirring until the mixture is smooth. You will need to knead in the last of the powdered sugar with your hands. Add food coloring; knead until the food coloring is evenly distributed.
Form the cream cheese mixture into ¾-inch balls, Roll each ball in granulated sugar; place on a waxed paper-lined tray. Flatten each ball with the bottom of a glass or very lightly with the tines of a fork. Cover the mints with paper towels; chill overnight. Store, tightly covered, in the refrigerator up to 2 weeks or freeze up to 1 month.