PLACE cookies on work surface, one above the other one, to resemble snowman. Attach cookies to each other with vanilla frosting.
CUT 1 end of 1 of the sticks of gum to resemble the fringe on a scarf. Trim other end to 3/8-inch width. Wrap scarf around snowman's neck.
CUT 2 triangles from remaining stick of gum; attach to snowman with frosting for the eyes. Place small dot of the remaining frosting in the center of each triangle; sprinkle with blue sugar. Add chocolate chip for the nose and roll candies for buttons on the body, securing each piece with the remaining frosting. Draw a mouth on the snowman's face with the red icing. Let stand at least 1 hour or until frosting is dry.