Anconas are a Mediterranean breed, and most, if not all, Mediterranean breeds aren't cold hardy. Yes, people in cold climates do keep them and they do just fine, but talking Alaskan cold, they might have a harder struggle. And, unfortunately, Mediterranean or not, most "great" layers aren't built for cold either.
If I were to suggest anything, I'd go with an Australorp or a Red Sex Link, or as the previous poster recommended, RIR. I've kept those breeds (single combed) and they do fine in the cold, though the bigger combed ones (which are typically your best layers) will be frostbite risks.