I ran directional treads backwards on the front, which caused tire store folks some consternation until I explained it. (You do 100% of your steering, and 90% of your braking with those tires, why would you want the tread facing for best traction toward the rear?) They got it.
I have been off the road (unplanned excursions) twice in nearly 40 years, and I drive in conditions up to and including white-outs.
Both times were on black ice, and on that you are just along for the ride if you do anything sudden (steer, brake, speed up or slow down). If you find you are on it and are still in control, relax and keep doing what you are doing. decelerate slowly, if that makes you fell better, and always avoid driving in a crowd if possible--where you will be forced by other people to react in ways that can cause you to lose control. You may have better control with studded tires, but I run the same skins year-round (Summer means mud...) and studs have to be off some time in April.
NYS winters aren’t much different in length and no different in quality.