Heat oven to 350°F. Lightly spoon flour into measuring cup; level off. On floured surface, knead flour into sugar cookie dough until well combined. Form pieces of dough into 3/4-inch, 1-inch and 1 1/4-inch balls. On ungreased cookie sheet, arrange 1 ball of each size in a row with smallest ball on top and largest on bottom, edges touching. Repeat with remaining dough to form 16 snowmen.
Bake at 350°F. for 11 to 18 minutes or until light golden brown. Cool 1 minute; remove from cookie sheet. Cool completely.
Frost cookies 1 at a time, and immediately press coconut into frosting. Press chocolate chips into frosting to form eyes. Cut gum drops into tiny carrot shapes; place below eyes to form nose, pressing in gently. Cut licorice into small pieces; place around neck to form scarf. Place 3 chocolate chips in a row below scarf to form buttons. Place peanut butter cup half on top of head, cut side down, to form hat.