To make these Christmas Eggnog Sugar Cookies gluten free, replace the all-purpose flour with a certified gluten-free 1:1 baking flour blend that contains xanthan gum. Be sure to check that the baking soda, extracts, cinnamon sugar, and any icing ingredients are also certified gluten free if needed for strict dietary requirements. Because gluten-free dough can sometimes be softer or more delicate, chilling the dough thoroughly before rolling and freezing the cut cookies before baking is especially helpful for maintaining clean shapes.