At least it sounds like the car is not too badly damaged. I'm guessing your pride was more damaged as all those cars streamed by.
I know exactly what you mean though. I drove an '89 Firebird Formula 350 year round for about 10 years in Chicago winters. For a few winters, I had Goodyear Eagle GS-Cs which are extreme performance summer tires. Of course, I had no idea that they were summer only tires. Here's what they look like:
Tire Rack link
As you can imagine, high hps and torque with a limited slip rear end, and FR format, coupled with these wide tires with absolutely no sipes, made winter driving a challenge. I got stuck a couple of times, but mostly it was on ice. I did enjoy starting from a stop though. As soon as I eased pressure off the brake, the rear end would start coming out one way or the other. It would stay that way (or sometimes go from side to side) until I picked up some speed. Needless to say, other cars gave me lots of room.
Driving up hills in the snow required picking up speed before hand in order to have the momentum to make it. If I had to stop on even the slightest hill (overpasses are a good example), I would generally end up letting the back end come all the way around, then crank the wheel into the spin to move it over into the lane going the other direction, and just go back the way I came. I got very good at planning my route while driving to avoid any hills. It was always a white knuckle ride when there was snow on the ground though. I wouldn't want to do it again.