More weight INCREASES stopping time and creates a less agile vehicle. The only thing increasing the performance of a vehicle in snow conditions in the tires.
"The braking comparison measured the tires' ability to provide traction during an ABS-assisted panic stop in a straight line. We drove the two Cayennes side-by-side at a speed of 30 mph, gave both drivers a braking signal at the prescribed mark and compared the distances it took them to come to a complete stop. The winter tire-equipped Cayenne stopped in an average distance of about 61 feet, while the all-season tire-equipped Cayenne took 102 feet (an additional 41 feet or about two and one-half car lengths). A 41-foot difference in stopping distance during a panic stop at 30 mph on a snow-packed road is more than enough to determine whether it's a near miss or an accident!
Additionally, while the all-wheel drive Cayenne offered noticeably faster acceleration than the rear-wheel drive sedan, the winter tire-equipped BMW's 59-foot stopping distance and all-season tire-equipped 89-foot stopping distance showed that all-wheel drive didn't really offer a measurable advantage when it came to stopping."
That was a test conducted with a very heavy AWD Porsche Cayenne with all-seasons. The BMW they speak of is a considerably lighter RWD sedan with snow tires. From a speed of JUST 30mph, it took an additional 43 feet to stop the AWD SUV with all-seasons than the 2WD sedan with snow tires.
A vehicle with snow tires will have 40% increased traction over the same vehicle with all seasons. This will translate to decreased braking distances, higher possible turning speeds and increased acceleration. All three of these are synonymous with increased safety and driving performance.
Again, from someone who drove a FWD Toyota Camry with snows and a Subaru Legacy Outback with All-Seasons, I would choose the FWD with snow tires EVERY time if snows on the AWD are not an option.