Preheat oven to 375°. In a large bowl, cream butter and confectioners' sugar until light and fluffy. Beat in egg and vanilla. In another bowl, whisk flour and salt; gradually beat into creamed mixture.
Divide dough in half. Mix Red Hots and cinnamon into one half; tint with food coloring if desired. Shape 1-1/2 teaspoons plain dough into a 4-1/2-in. rope. Shape 1-1/2 teaspoons red dough into a 4-1/2-in. rope.
On an ungreased baking sheet, place ropes side by side; press together lightly and twist. Curve top of each cookie down to form handle of cane. Repeat with remaining plain and red dough, placing 2 in. apart on baking sheets. Sprinkle with coarse sugar.
Bake 7-10 minutes or until lightly browned. Cool on pans 1 minute. Remove to wire racks to cool. Yield: 4 dozen.