Proper winter tires are your best bet. Studs help on pure ice, but for everything else a non studded winter tire is about the same. I run winter tires on all of my cars and some are studded and some are not, so this is from personal experience. I would never drive an all season on snow again. The only downside to studs is noise on dry pavement and added cost.
As you've found, traditional style MT tires like those are very poor in the winter.
In Anchorage, it would be worth it to have a set of winter tires. In addition to tread design, the compounding handles the low temperatures much better.
For the Defender, I would suggest the Nokian Hakkapeliitta LT with or without stud depending on your choice.