Cream together butter and shortening. Add confectioners sugar, egg, and extracts.
Blend flour and salt. Add the flour mixture and blend on low spread until incorporated.
Divide dough into 3 sections and mix red food coloring into one, green into another, and leave one plain.
Wrap dough separately in plastic wrap and place in refrigerator for at least 1 hour.
Flour rolling board. Using fingers, roll a pinch of two different color doughs into long ropes. Twist ropes together and hook one end to form a candy cane. Transfer to cookie sheets.
Bake at 375° for 10 minutes or just golden.