It's not so much about the tires, but rather the competence of the driver.
From 1997-2004, I drove an old 1971 Plymouth Valiant, one of many old 1970's Chrysler cars I owned and worked on for many years. The body was rusted but the drivetrain was awesome. With an 8-1/4" axle and rebuilt 3.21 limited slip differential, and an old set of winter tires with the treads that went way out to the edge of the tires and made a 90 degree turn to the sidewall (the super chopper shredder tires, as I termed them), that car would go just about anywhere. Even up old muddy wet snowy dirt roads on hills. In snowstorms, it was fun to be first in line at an intersection where I was turning left, I'd just lock it in second gear, get the tires spinning on snow covered roads when the light turned, and just do a nice, slow, controlled sideways drift through the turn. All at a vehicle speed under maybe 20 mph or so.
Now you can't run bald tires in the winter and expect much to happen, but if you're crazy enough, you can get around. Way back in those days, my tires weren't considered "worn out" until I got down to the second layer of steel belts showing somewhere on the tire. Then they got changed, not for new tires, but for "good used, less worn out" tires.