Grease and flour 2 layer pans, one 8 x 1 1/2" and one 9 x 1 1/2". Prepare any flavor layer cake mix as directed on package except divide batter evenly between pans. Prepare fluffy white frosting mix as directed on package.
On aluminum foil-covered cardboard, place 8" layer for head of snowman and 9" layer for body. Frost layers, joining them together. Sprinkle with flaked coconut.
Use semisweet chocolate pieces for buttons, gumdrops for eyes, eyebrows and nose, red shoestring licorice for mouth and red rope licorice for muffler. Place large chocolate wafer cookie on each side of head for earmuffs.