You logic is good, but the reality is that you’re going to have to select from what’s available that you can afford. I’ve been driving 2WD vehicles in winter weather (including the Rochester area) for 45++ years, and the most critical thing is that the vehicle is in good shape, properly winterized, AND, in that area you should have GOOD winter tires, (“good” meaning no less that 2/3 of the tread). That area gets nasty lake-effect snows.
Proper winterization means the aforementioned snow tires, “winter mix” windshield wash mix (keep the wash container filled), proper coolant, good ignition parts, and good non-icing winter wipers. I’ve found “blade” style wipers to be the best. You’ll also need a good scraper, good snow brush, and I recommend a plastic bottle full of dry sand for use on ice. I use a large Gatorade bottle. Also be sure you keep your headlights and windows clean. I don’t know if it’s a law in the NY State, but in NH you also must clear the snow from your hood, trunk, and roof before heading out (in addition to your windows, of course). Ice sheets flying off cars can and do kill others.
Others here will, I’m sure, add to the items.
In short, more critical than AWD or 4WD (great if you can afford them) is a good vehicle in good shape, winterization, and a few winter items in the trunk. And good sense. No powertrain on earth is as good as knowing when to stay home. Since you’ll be a college student, allow me to recommend that you live either in the dorms or within walking distance from your college.
Sincere best of luck in your academic career. Do well.