AWD can make a difference when starting from a stand still in snow, it can be quicker off the mark vs a FWD with winter tires and could get our out of a tricky spot if the rear tires have a bit better purchase on the surface than the front. Problem with FWD is if you don't get going in your first attempt, tire spin can turn snow to ice, and then you need to either rock the car and judge when to use power (a fun challenge) or back up to get back onto sticker snow. I'm just saying that there are occasions when AWD can be better.
Many people are getting snow tires and winter (cold weather) tyres mixed up here. We are talking about cold weather tires which are designed to help just as much in cold temperatures, dry or wet. So if you don't get much snow you shouldn't write them off straight away! If your average winter day are below 44F, the cold weather tires will start to benefit in any road condition.
Of course, regular snow means it should be a no brainer, or like many countries, when it is the law. In the end, a massive piece of how your car will perform comes down to the driver. I spend hours on the roads when they are covered in snow playing in my car, seeing how fast it will go from 0-60, with or without traction control, seeing how long it takes to brake, of course, this is late at night and in the middle of nowhere. All cars here have winter tyres, but you still see plenty off accidents, mostly people not leaving enough gap to stop or thinking ABS is a magical device.
I took my STI out one evening into the forest, 2ltr turbo, AWD with winter tyres, was a 2001 555 special addition, about 1ft of snow, great fun, I thought I was Colin McRae (went to school with him). Ended up in a ditch, got out eventually, no harm done apart from massive vibrations in the car, after a few days the temperatures rose enough for this massive lump of ice to thaw from around the read drive shafts...all good fun.
Someone mentioned that they were driving too fast in the video for the conditions! Exactly my point, you need to try your car beyond the limits (safely) to understand where the limits are and to see how the car behaves. In the US there are plenty huge parking lots to test you winter driving.
I bought AWD because it is my wifes car, she is not a bad driver (I hope she never reads this) but I think her and my daughter are safer with AWD. There are a few junctions close to use that are often covered in snow and ice, you need to cross 3 lanes of traffic coming the other way and AWD is just a safer choice, I don't car for the weight penalties or mpg.
An old video, but one of the better ones....
https://www.youtube.com/watch?v=7l2cMlNRX_A