In a large bowl, combine butter, flour, and confectioners' sugar. With an electric mixer, beat for 10 minutes, until light and fluffy. Spoon onto cookie sheets, spacing cookies 2 inches apart. Place a piece of maraschino cherry onto the middle of each cookie, alternating between red and green.
Bake for 15 to 17 minutes in the preheated oven, or until the bottoms of the cookies are lightly browned. Remove from oven, and let cool on cookie sheet for 5 minutes, then transfer cookies on to wire rack to cool. Store in an airtight container, separating each layer with waxed paper.