Place butter in large mixer bowl. Beat at low speed until creamy. Add powdered sugar, whipping cream and peppermint extract. Continue beating until mixture forms soft dough.
Divide dough in half. Beat red food color into 1/2 of dough. Continue beating until dough is pink. Beat green food color into the other half of dough; beat until dough is light green.
Knead each tinted half of dough on surface lightly sprinkled with powdered sugar until smooth. (Keep doughs covered with plastic food wrap to prevent drying out) Roll 1 tablespoonful of each tinted dough into 4 inch rope. Gently twist green and pink ropes together. Carefully continue rolling and twisting rope to 10 inch length. Add more powdered sugar when rolling, if necessary. Cut diagonally into 1 inch pieces.
Place twists on waxed paper-lined baking sheet. Let stand uncovered at room temperature until surface is dry. Layer mints between sheets of waxed paper in airtight container. Refrigerate up to 1 month. For longer storage, store in freezer up to 2 months.