Clarification: Winter rated tires.

There are all-seasons (the Nokian Haakapalitta tires I've mentioned) that are incredible in the winter (actually best tire I've ever driven in bad conditions, deep snow and winter-long ice).

But to your point, while you can run them in dry conditions, they will wear much faster than typical all-season tires due to the softer compound.

There's no other all-season tire I've used that actually works in snow or ice, let alone as well as Haakapaliitas.

But if you have a long winter, I'd get a set of their dedicated winter tires and switch seasonally as you said.