To make our delightful Drunken Snowman Cocktail gluten-free pay attention to the chocolate mix, which is the key ingredient, in our recipe. Many hot chocolate mixes contain gluten as a thickening agent so choose one that is clearly labeled as gluten-free. These types of mixes are often made with cocoa and sweeteners without any additional fillers or ingredients that contain gluten. Also make sure that your vanilla ice cream and Bailey's Irish Cream are free, from gluten as some brands might use flavorings or additives that contain it.