Why? FWD has better traction because more weight is over the drive wheels, and it's more stable (when rear drive wheels slip the car fishtails).
Depends on the weight distribution in the particular car. Drive something like a BMW where the weight distribution is close to 50/50 and you don't have such an advantage from FWD. The type of drive system (FWD, RWD, AWD, 4WD) only actually matters when accelerating. FWD works better for many people for exactly the reasons you mention but a RWD rear engine car (porsche 911) can get excellent traction for the same reasons. Really you want AWD or 4WD if traction under acceleration is a big concern. But a good set of snow/winter tires will make a MUCH bigger difference than the type of drivetrain ever will for most vehicles.
As for tire width, I never noticed that
Generally speaking wider tires often perform worse in snow all other things equal because they don't penetrate through the snow as easily. There are plenty of exceptions but they tend to float over the snow rather than penetrating down to pavement.
The cut of the tread is another matter.
It's not just the cut of the tread. It also is the rubber compound that matters. Snow tires don't get as hard in colder temperatures in addition to usually have different tread properties. They make a HUGE difference even in relatively modest amounts of snow. In many places a good all-weather tire can perform adequately but you will notice an improvement in sloppy conditions with a set of snow tires.
About the only problem I know of with FWD in slippery conditions is that the weight gets transferred to the rear when going uphill.
You'll always have the same problem when accelerating because the weight shifts to the rear tires when you accelerate. This is why FWD cars make rather bad dragsters. You don't typically notice in your boring family sedan because the car doesn't have enough power for it to matter much. Many RWD vehicles are poorly balanced in order to make them understeer so the weight distribution is too far forward. But it doesn't have to be that way and isn't in some RWD cars. I would actually argue (from my own experience) that a well balanced RWD car is easier to drive in the snow than many FWD cars.