In a mixing bowl, combine sugar, butter, egg yolk, and vanilla. In a second bowl, combine flour, cocoa powder, and salt. Add the wet ingredients into the dry ingredients, stirring until a thick dough forms. Divide in half and wrap in plastic. Refrigerate 30 minutes or until very cold. (If you refrigerate the dough too long (or overnight), it will get too stiff to work with. It will soften up again if you let it sit on the counter for 10-15 minutes.)

Heat oven to 350F. On a floured surface, roll dough to 1/4 inch thickness. Cut out with snowman-shaped cutter; arrange on a baking sheet. Gently press a lollipop stick into each cookie; use scrap of dough to hold the stick in place. Bake 14-16 minutes, or until set. Let cool.

Frost cookies; immediately cover hat area of snowmen with cookie pieces. Use additional cookie pieces as buttons and eyes. Draw on a scarf with decorating icing.