I haven’t used studded tires for many years, but I recall that they were very effective on ice, less effective on snow, and not very good for everyday driving. In addition, they damage roads. I can recall some very serious damage to my parents’ driveway, which had a considerable incline, and this was caused by my studded snow tires.
I would recommend that you get a set of 4 winter tires (the term “snow tires” is somewhat archaic at this point) mounted on their own steel wheels. Winter tires are actually fairly effective on ice, unlike the old snow tires, and unlike the so-called “all-season” tires. Most important of all, a set of 4 winter tires will allow you to stop the car in a much shorter distance than you can currently, and will help to keep you on track on turns.
Gas mileage will probably be worse with any winter tire, as compared with so-called “all-season” tires, but that is part of the price of additional safety. As it is currently, you have a serious traction difference between the front and rear tires, and that is likely to lead to the car’s rear end winding up in the front when the car spins around on a slippery surface as a result of this serious traction differential.
Incidentally, when you mount winter tires, it is beneficial to get tires that are one size narrower than your current tires. A narrower winter tire will be less likely to ride on top of snow, and more likely to be able to “cut” through the snow. This may sound counterintuitive, but it is a fact. Your Owner’s Manual should list acceptable “alternate tire sizes” in order to give you an idea of just how much narrower you can go without compromising the load-carrying capacity of the tires.