In large bowl, combine margarine, sugar, egg, milk and vanilla; mix until light and fluffy. Lightly spoon flour into measuring cup; level off. In medium bowl, combine flour, baking soda and salt. Add flour mixture to margarine mixture; mix well. Place half of dough in plastic bag or wrap in plastic wrap. To remaining half of dough, add peppermint extract and red food color; mix well. Place in plastic bag or wrap. Refrigerate both portions 1 hour.
Divide each portion of dough in half. Roll 1 part white dough between 2 pieces of plastic wrap; roll into 10x8-inch rectangle. Repeat with 1 part pink dough. Remove top sheets of plastic wrap from white and pink dough. Place pink dough over white dough; remove plastic wrap from pink dough. Trim edges, if desired. Starting at 10-inch edge, roll up dough jelly-roll fashion, removing plastic wrap from bottom as dough is rolled. Repeat with remaining dough to form second roll.
Place 2 tablespoons of the pink sugar on separate sheet of plastic wrap. Roll 1 roll of dough in pink sugar, pressing gently into dough. Repeat with second roll. Wrap rolls in plastic wrap; refrigerate 8 hours or until firm.
Heat oven to 375°F. Cut dough into 1/8 inch slices. Place 1 inch apart on ungreased cookie sheets. Bake at 375°F. for 5 to 7 minutes or until light golden brown. Cool 1 minute; remove from cookie sheets.