I am certainly no expert on New Mexican cooking, although we love buying fresh, warm tortillas at the local tortilleria; and we wouldn't miss getting our big bags of freshly roasted, locally grown green chiles every fall at the Farmer's Market. Right now, the grocery stores are featuring displays of pork shoulders, dried red chiles, and posole corn--a hint to me that I had better start learning how to make a big pot of posole.
To give you an idea of Christmas cooking here, the best thing I can do is to send you to this article by Nancy Gerlach on the Fiery-Foods.com website. It includes recipes for Green Chile Tortilla Pinwheels, Chile de Arbol Salad, Posole (Pork and Posole Corn), Red Chile Sauce, and Biscochitos (Anise-Flavored Cookies). There is also a discussion of the origin of farolitos, or luminarias--different areas of the state call them by different names--the little candles in paper bags that line walkways and roof lines at Christmas.
I was a little surprised that the Fiery-Foods article didn't give a recipe for tamales, because as this piece from Texas Cooking tells us, "It's Not Christmas Without Tamales." Remember, they call this area Little Texas, so I guess it's okay for us to reach across the border for some Texan recipes, too.