The thing I have found living in both Colorado and Upstate New York is that its all about small, smooth movement with the wheel, brakes and accelerator. You can cruise along at a pretty good clip with this attitude. Just focus on being very light with the touch, especially with the brakes.
I would say 90 percent of the accidents I have seen were cause by someone mis using their brakes, which causes them to slide out of control, at which time they try to over correct with the steering. Always have an eye well beyond where you currently are looking for patches of ice and snow drifts or whatever else might be ahead of you.
As for tires, especially for a place like upstate NY, I would highly recommend a set of at least studless snow tires. For some reason they don't seem to get used very much up there, with most people favoring All Season. In my experience though, All Season suck for all seasons for the sake of working sufficiently for them. Any All season worth a damn in either winter or summer won't be any good for the other. So I have my Summer and Winter setup (Ultra performance Summers and Blizzak studless snows for the winter).
The last thing I notice with winter driving is, that in a bad snow storm at night, the less lights you have the better. As much as I love feeling like I am in Star Wars driving through Hyperspace, its really really disorienting and sucks it big time. I have been in a couple situations where having no lights on at all was the highest visibility option. Its a bit unsafe if there are other cars on the road, so I often opt for just fog lights. That way you still see the road but you don't have lights pointing up into the driving snow.
I agree that having some fun in a parking lot is a good way to figure stuff out, but just doing donuts isn't going to help. Try starting a spin and getting out of it or keeping the car as straight as possible. See how long you can hold a drift. See what it takes the car to lose grip.
Lastly, I believe that unless the conditions are absolutely horrible, that at least trying to go the speed limit is advisable (keeping the soft touch in mind). Cars that go 5-15 mph will only cause frustration for other drivers, and if you are going to have a wreck at 25-30, you'll probably have it at slower speeds too. If you don't feel comfortable driving at normal road speeds, then you probably should have just stayed home and called in sick. Someone driving at slow speeds is just going to cause accidents, as people will want to pass or they'll come upon them and panic.
Ok, enough rant.....have fun in the winter. There are lots of fun roads to go play on and figure yourself out up in NY.
JH