I live in TN. Someone from up north mentioned studded or snow tires to me other day, I just laughed. Yeah, it doesn't pay for the minimal amount of snow we usually get, or that melts off the main roads within a day or so. I have a front wheel drive '07 Eclipse, and I just use that if I have to work/go out when it does snow here. Just use common sense, drive slower, don't brake suddenly, don't tailgate, and ignore those fools tailgating you. I grew up in Chicago, and learned how to drive with feet of snow on the road, with a rear wheel drive '85 Monte Carlo. Generally, nothing drives on ice. Looks like you had that sleet and snow on top of the ice-just like we did here, that gave you some traction on the ice. Just freezing rain or black ice, nothing's moving on that how it should.
What I used to do in my old RWD car, just load up the back with kitty litter, salt, at least a good 100 lbs. My old truck I had, I threw a bunch of landscaping bricks in the bed over the axle. If I approached a red light, I'd try to time it and slow down if I could to avoid stopping. That was always when I ran into problems, trying to take off after stopping. Carry a shovel also. And, I also would drop it into 1st or 2nd on the gear shift. Just keep that under 30 mph for 1st and under I think it was 55 mph for 2nd. When your in the market for a new vehicle, at least get a front wheel drive or all wheel drive. FWD should be good enough for your area though, and that's pretty much the norm on most vehicles now a days.