Hard disagree. I've got a couple identical wagons (same model, year and everything) and one of them is optioned AWD while another is optioned FWD. The FWD one gets snow tires every winter and it's still the crap one of the bunch. I bet if I constructed some tire commercial-esque test where I compared handling on a literal ice rink it might win but in real world driving conditions (snow under 6" that's been churned into partial slush by the melting action of road salt and the last bunch of cars) it's still second place.

I am comparing some of the cheapest all-seasons on earth to some of the cheapest snow tires on earth in a vehicle platform that was renown at the time for having one of the most effective AWD systems so if I were to compare high dollar all seasons to high dollar snow tires in a vehicle known for having particularly bad AWD the results may be different.

Tire quality makes all the difference. If you value traction and safety, please don't skimp on tires. Buy the good ones, the difference in braking performance alone is massive.