you can't possibly look at those two videos and tell me that a RWD BMW doesnt handle snow well. you will obviously have issues with traction if the snow is very deep, but any good-handling modern RWD car tests your driver skill with careful throttle, steering and braking input to the very limit and the results are astounding. the best part is that when driving civilized in the snow, the car steered and braked excellent and the rear end would never need to be corrected unless you go too hot into a corner and hit the brake before turning in, or stab the throttle as soon as you turn the car in and even then. it was so easy to control. the old Thunderbird you had is a lovely looking car and theres absolutely nothing wrong with the way it handled, but chassis balance and stability has come quite a long way over the next few decades that a BMW equipped with good winter tires is immensely capable while being very fun to drive.
I will admit, that my BMW was a death trap in the snow with all seasons because they were very bad tires and also quite worn which is why the car handled terribly initially. (funnily enough if you were going fast enough for aerodynamics to glue the car into the ground it drove quite well) another benefit of having winter tires - instead of having mediocore, or "just enough" grip year round and the convenience of not needing to switch tires, I can mount some proper summer tires when it's warm out and then switch to winter tires when the weather becomes cold so I can make the most out of my RWD chassis.as long as you have some sort of all-seasons that can actually handle snow, your AWD mazda will get around just fine without winter tires.