I’d be careful with that statement because we should really differentiate between the 2 types of winter tires. ”Performance winter” tires will definitely do better than all seasons in the cold/wet scenario, but those classified as “studless snow/ice” winter tires actually do worse in cold/wet than ultra high performance all seasons. I’ve compared countless charts on tirerack and have noticed this pattern pretty consistently.
If you live in an area where there is snow on the ground more days than not, then you should probably have a studless or performance winter tire. However, there are a lot of people that live in areas that only get snow a few times per year but still cold and wet and can’t run summers year-round. An ultra high performance all season should suffice for those folks year-round, but if you’re really concerned, a performance winter would be better than a studless winter tire for folks that live in those areas since wet traction is not great with studless winters.