I have been driving a Crown Victoria squad car for 6 years. Goodyear Eagle UltraGrip snow tires are not the best tire by any means, but I've done some amazing things with that car. Keep in mind that this is a RWD vehicle with an open differential and very hard performance snow tires. If it gets dicey out, I throw a couple 75lb sand bags in the trunk and it does wonders. I've driven through 18" of standing snow, gone up and down iced over hills, and turned a car sideways on a downhill curve at 40mph and corrected it without going into a ditch.
Now compare that to my old E46 M3 with a limited-slip differential, better weight distribution and Dunlop Winter Sport tires, which are better than the Goodyears. That M3 NEVER got stuck. I had H&R springs on it and I still plowed through 12" of snow with it. It was a mountain goat.
If you went to a snow/ice tire like a Blizzak WS70 or Dunlop Graspic, you'd do even better.
Tires make a huge difference. I've driven Maseratis with Sottozeros, and they pretty much suck for anything other than highway use. As has been said, they are more like softer all-seasons than actual snow tires. The Pirelli WinterCarving tires are okay, but the Sottozero is a performance tire with limitations. Given a comparison to another performance snow tire like the Blizzak LM60, the Blizzak is far and away superior. Look at the TireRack.com surveys and see the massive difference.
Michelin PA3 1 $199 100% 8.2 8.8 8.9 8.6 8.8 8.7 8.7 7.9 7.8 8.8 8.6 8.3
Sottozero S-II 5 $193 98% 8.1 8.7 8.9 8.3 8.5 8.5 8.5 7.6 7.8 8.9 8.3 8.3
Blizzak LM-60 8 $209 96% 8.8 8.4 8.4 7.6 8.0 7.7 9.3 8.8 8.3 8.2 7.6 8.0
The LM-60 is highly underrated in this survey, but notice that it has better snow and ice traction than even the #1 PA3. It blows the Sottozero out of the water in every WINTER category. Look at the major differences with light snow, deep snow and ice. It's a world of difference.