Combine butter and sugar in a large bowl. Beat at medium speed until creamy. Add 1/3 cup eggnog, egg and vanilla; continue beating until well mixed. In another bowl blend the flour, bkg. powder, nutmeg and salt. Put mixer on low and start adding the flour mixture. Mix until well blended. Now divide the dough into two disks and wrap in plastic and refrigerate for at least 1 hour.
Pre-heat oven to 375º Roll out dough one disk at a time. Cut out with snowman cookie cutter. Bake for 8 to 12 minutes. Every oven is different. Cookies should be light in color. Frost with white icing, then divide rest of the frosting into the colors you want and continue to color your snowmen. Decorate with mini choc. chips or red dots.