[Phred]

I concur, I've heard lots of seasoned drivers boast about how great their cars went through the snow "back in the day". "Those narrow tires just cut through to the snow..."
My experiences with both a '37 Plymouth and Model A sedan were more similar to yours, the car did not handle well.

I suspect the people telling about those times do not mention how their cars were prepared for the snow (additional weight, snow tires, and/or chains). In short, our cars may not be as "prepared" for the snow as they used to be.