I see Jersey schmucks up here with their pavement princess trucks getting stuck in the snow all the time. I see locals in a Corolla or fiesta or other tiny light car make it just fine in deep snow. One of my bosses at the ski mountain used to drive a mini Cooper an hour to work every day.
Skinnier tires are actually better in snow because they can dig down to the ground somewhat and find traction there. Wide tires tend to float on top of the snow because of the larger contract patch (but not enough to stay above it, that requires huge, under-inflated-balloon-like tires like what you'd need on an antarctic expedition)
Growing up my mom lived on one of the biggest hills in a town that was basically all hills. She remembers when it snowed they'd watch all kinds of cars and trucks get stuck trying to make it up that hill, and then watch a guy in a little VW beetle go right up the hill like it was nothing, perfectly happy will of that engine weight right over the rear drive wheels.
Years later I'm a new driver borrowing my parents's cars, a '93 RWD ranger, and a '92 Buick century, and that comparison did a good job of driving home how much difference that weight distribution matters. The ranger had some pretty good grippy tires, but without any weight in the bed, it didn't take much to make those wheels spin. The buick, on the other hand, handled snow beautifully, it had all the weight of that big boat-like front end over those front drive wheels, never once struggled to find traction, the only limiting factor was that it sat pretty low to the ground so it didn't take too much snow before that front end was just trying it's damnedest to plow through snow. If some mad scientist ever thought to lift an old Buick a few inches, I'm pretty confident that 4wd/AWD would become all but obsolete.
One of the most satisfying things for me is driving my wife's little Mirage in the snow. With normal all season tires it does great, with proper snow tires it's completely unstoppable - that is, until you need to stop.
It turns out that accelrating and stopping a 2,000 pound car on ice and snow is easier than it is with a 4,000 pound vehicle.
skill? sometimes. the fact that those corollas and mini coopers only weigh a fraction of those huge trucks probably has something to do with it, too...
Weight and weight distribution are both important, but a pickup will usually perform better in snow with more weight, like 500 lbs of sand in the bed usually does the trick.
How you apply power to the road surface is also very important. Not enough weight and you will just spin tires. Break too aggressively and you lock up. Pedal to the floor and your tires are spinning. Overcorrect your turns when you start to slide and you'll never get back straight.
My car is a little older and actually drives better in snow with the traction control off.
but they have much larger, heavier engines and drivetrains.
a ford f-150 weighs about 4,500 lbs (minimum). a dodge ram weighs about 4,750 lbs (minimum)-- these are without any outrigging which can almost double the weight.
a corolla and a mini weigh about 3,000 lbs. a ford fiesta weighs about 2,750 lbs.
those are pretty big differences (to start) which can get bigger depending on the configuration of the truck.
They are heavy but the weight distribution isn't even and most trucks are 4x4/RWD which is what leads to the issues you're alluding to. The rear tires can't propel the vehicle because there's not enough weight over them in the rear compared to the weight of the front.