I went poor and didn't put the snows on. I figured that the 2000 mile old tires I have on my car are better in the snow than my 2 corded and 2 bald snow tires.
Also note that I DID NOT HIT THE CAR IN FRONT OF ME, nor did I come close to doing so, nor did I go into the other lane where there was traffic going the other direction. I probably didn't come within 30 feet of the car ahead at the closest point. Because of how the road is cambered and how slick it was, had I stopped going forwards with the car in the lane I was in pointed in the correct direction, the car still would have slid sideways off the road into the snowbank. The road really was that slick, and there really was that much banking in the road at that point. I have enough experience with all types of tires in all kinds of conditions to determine whether snow tires would have helped, and in this case, they would not have.
ChesterWRX sounds amazingly like a cop I encountered about 15 years ago after I hit black ice going 20 MPH and went off the road (in a FWD car that I had run HPDE events with, and was very familiar with, with snow tires, on a corner marked by a yellow sign at 25 MPH), who said I was going "too fast for conditions". So I asked him how fast was appropriate in that situation. He couldn't give me an answer, probably because when he hit the ice at 10 MPH, he went off the road into a snowbank, and he slipped and fell on the road when he got out of the car because of the ice.