Beat butter in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add sugar and beat until combined, scraping sides of bowl occasionally. Beat in egg, water, and peppermint extract until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon. If desired, stir in red or green food coloring. Cover dough and chill in the refrigerator about 2 hours or until firm enough to handle.
Preheat oven to 350 degree F. Divide dough into 12 equal portions.
Roll each portion of dough on a lightly floured surface into a 12-inch-long rope. Cut ropes into 3-inch-long logs. Place logs about 1 inch apart on an ungreased cookie sheet. Lightly press three or four candies or chocolate pieces into each log.
Bake in a 350 degree F oven for 12 to 15 minutes or until edges are firm. Transfer to wire rack; cool. Makes 48 snacks.