A winter-rated all-weather (not just "mud & snow") might make strictly financial sense if you do very low mileage and/or don't keep the car long. It might also make sense for the last year or two of ownership if both your winter and all-season sets are too worn to drive. However, that's not the choice I'd make.
We both live in Quebec, where there's a "real" winter. If you're going to drive long enough to wear out your all-season tires, you might as well extend their life by using a dedicated high quality winter tire - you're initially paying more, but you're also extending the life of the all-seasons. You'll also likely be able to get smaller (and less expensive) wheels and tires and a narrower profile for the snow.
Ultimately, even if a set of premium winter tires does cost more (and it's not that much more over the entire life of the vehicle), the safety of my family is worth more than saving a few hundred bucks on tires. No one tire is perfect for all weather, especially in a northern climate. As you probably know, its not just about thread patterns in snow - it's also about how some rubber compounds are softer and have more grip below 7°C.
What makes winter tires so effective? It's the perfect mix of ingredients, plus a grippy tread