Bruce Hirabayashi and Leo are the tire gurus. Let's let them comment before we amateurs do.
I agree however about your choice of tire. If it's strictly performance you are going for - no holds barred - then you want the big rims with the slim, stiff tires. The thicker wheels and a slightly "softer" suspension will take a way a touch of the road feel and dampen the response a bit, but... they take away a touch of the road feel and dampen the response.

You have to optimize your performance for something. Optimize for offroad or deep snow and you aren't going to be doing 140 on the Autobann. Optimize for the Autobann and you aren't going to be 4-wheeling it offroad in the mountains. Optimize for a pimpmobile ride and you'll feel like your car's on novocaine when doing the slalom. Optimize for longevity and you sacrifice the quality of an athletic ride. Etc.
Some of the newer technologies (like the tire Leo showed us) would perhaps broaden the capabilities a bit so you don't have to sacrifice so much in one venue to get optimum in the next. And I particularly like some of the newer supsensions that adapt to your driving at the moment and even are manually adjustable.
As for the AWD and the Richmond ice scenario... Yes, it absolutely would help some - as long as you stay away from the person 3 feet to the left who's now driving backwards.
Leo (I believe) alluded to the nonsense of people gunning their cars to get up a slippery hill. Those who have a feel for it all and those who understand physics understand that the smarter thing to do (barring high technology) is to start your vehicle in 2nd gear and proceed gently and evenly. The issue here is static friction vs. kinetic friction. Static friction is what keeps your tire and the road from moving with respect to each other. There is a "breakaway" point where you start to slide. That's sometimes referred to as the coefficient of static friction. Once you have lost traction, you now are in the realm of kinetic friction. These are the "sheer forces" when one surface moves with respect to another.
The coefficient of static friction is larger than the coefficient of kinetic friction. This is an important concept to understand. Basically it means you want to prevent yourself from sliding in the first place. Once you start sliding, bad things can happen.
In a classic FWD or RWD system, all the torque goes to either the 2 front wheels or the 2 rear wheels. That torque exerts a force on the wheels which moves the car with respect to the pavement beneath it. As long as the force exerted by the wheels against the road is less than the coefficient of static friction, you will not slide and your vehicle will move in a well-behaved fashion. Once you break the static bond between tire and road, it's harder to get it back and it's much more difficult to control the vehicle.
With AWD, you distribute the torque amongst all 4 wheels. The BMW X-Drive system pioneered an AWD system where most (close to 70%) of the torque goes to the rear wheels, This helps maintain that RWD feel, which keeps you from understeering in sharp turns and prevents the feel of acceleration fighting with steering. Other drive systems (the ATESSA system form Nissan, the simple system in the 300C and Magnum from Daimler Chrysler) have since copied this RWD bias configuration.
Anyhow by distributing the force amongst all 4 wheels, you're less likely to break traction in any one wheel. As long as you don't break traction, none of the fancy electronic controls need to come into play.
But this is where it gets better.
BMW's X-Drive system is capable of adapting when it senses one wheel has broken traction. When that happens, the system disconnects the torque from that wheel, and sends it to the others. So if you hit a small patch of ice, at least one wheel is likely to maintain traction and you're probably not going to experience ice-skating driving. The Germans are leaders in this technology. BMW, VW/Audi, and Mercedes all have competing systems that work to redistribute torque to wheels other than the wheels that are slipping. They each do it in a slightly different fashion. Nissan has its own unique version that is kind of interesting. But they all are much better than not having that extra compensation.
As long as you remember that AWD does not mean AW stop, you're much better off than the next person on the road.
- Bill