In a large bowl, cream butter and confectioners' sugar until light and fluffy. Beat in egg and vanilla. Combine flour and salt; gradually add to creamed mixture and mix well. 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 at 375° for 7-10 minutes or until lightly browned. Cool for 1 minute before removing to wire racks to cool completely. Store in an airtight container. Yield: 4 dozen.