Let cookie dough stand at room temperature for 5-10 minutes to soften. In a small bowl, beat the cookie dough, flour and extract until combined.
On a lightly floured surface, roll out dough to 1/4-in. thickness. With a floured 4-1/2-in. round cookie cutter, cut out two circles. Repeat with 3-1/2-in. and 3-in. round cookie cutters. Cut out six 1-in. circles, four 1-3/4-in. mittens and two 2-1/4-in. carrots.
On waxed paper, draw a top hat, 3-1/2 in. wide x 2-1/2 in. tall and a pipe, 3-1/4 in. wide x 1-3/4 in. tall; cut out. Re-roll dough scraps if necessary. Using patterns, cut out two hats and two pipes.
Transfer pieces to greased baking sheets. Bake at 350° for 6-11 minutes or until edges are lightly browned. Remove to wire racks to cool completely.
Tint frosting as desired; frost over cookie pieces. Let stand until set. Store in an airtight container. Yield: 2 snowmen.