1. Preheat oven to 350 degree F and butter 4 large cookie sheets.
2. Roll 1 disk of dough on a lightly floured surface with floured rolling pin until 1/4 inch thick. Cut out dough with a 5-1/2-inch snowman cookie cutter, gather scraps of dough into a disk and re-chill until firm. Transfer cutouts to prepared cookie sheets and chill until firm, about 15 minutes.
3. Repeat rolling, cutting, and chilling remaining dough and dough scraps in same manner.
4. Bake and cool cookies in same manner as snowflake cookies.
5. Melt chocolate with butter in a metal bowl set over a saucepan of simmering water, stirring until melted. Remove bowl from pan and let cool to room temperature.
6. Brush tops of Snowmen Cookies with chocolate mixture and sprinkle with coconut. Transfer cookies to a cookie sheet in one layer and chill until chocolate is firm.
7. Cookies will keep for 2 weeks stored between sheets of waxed paper in an airtight container at room temperature. Makes about 4 dozen large cookies.