Preheat oven to 375 degrees F (190 degrees C). Lightly grease a baking sheet.
Stir the flour, cornmeal, sugar, baking powder, and salt together in a mixing bowl until blended.
Cut in the butter using a pastry cutter or two knives until coarse crumbs form.
Mix in the craisins. Use a fork to stir in the eggnog and make a sticky dough.
Turn the dough out onto a lightly floured surface; dip hands in flour and knead the dough about 10 times. Pat the dough out into a disk about 1/2 inch thick. Dip a 2 inch diameter biscuit cutter into some flour, and cut out 8 to 10 rounds.
Place rounds about 2 inches apart on prepared baking sheet. Use up remaining dough by patting it into a smaller disk and cutting again.
Bake in preheated oven until risen and golden brown, about 15 minutes.