In a large bowl, cream together the margarine, white sugar and confectioners' sugar. Beat in the egg, vanilla and peppermint extracts. Combine the flour and salt; stir into the creamed mixture until well blended. Cover or wrap dough and chill for at least one hour.
Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets. Divide dough into halves. Color one half red by mixing in the food color. Roll a small amount of each dough into a 2 inch long worm. Roll them together in a twisted rope and curve the end like a cane. Place onto prepared cookie sheets.
Bake for 8 to 10 minutes in the preheated oven. In a small bowl, mix together the crushed candy cane and remaining white sugar. Roll hot cookies in the sugar mixture.