In the bowl of an electric mixer, cream together butter, shortening, and powdered sugar on low speed.
Add the egg and vanilla, and mix until well incorporated.
In a separate bowl mix together flour and salt, and then gradually add them to the wet ingredients, mixing on low speed until a smooth dough is formed.
Remove half of the dough from the mixing bowl, and set aside. To the dough remaining in the bowl, add a few drops of red food coloring and mix to distribute.
Form 24 teaspoon sized balls of each color of dough.
Roll each ball into a four inch tube, and pair them side by side on an ungreased baking sheet.
Twist the red and white dough together and form into a candy cane shape.
Bake for 10-12 minutes, and remove the cookies to cool on a cooking rack.
Whisk powdered sugar and milk together until a smooth glaze is formed. Spoon over cooled cookies, and sprinkle with red decorating sugar.