I used to drive 85000 kilometers a year (mostly between September and the March time frame) so I know a thing or 2 about winter rubbers.
There are 2 ways winters rubbers will get through snow,
1. Skinnier tires will have less material to disperse.
2. Plus if the sides are softer, the thread will flex better to release the sticky snow that can get stuck in the thread making the tires slipperier than they should be.
As for Ice there are also 2 ways the tires act better,
1. A rubber compound that remains softer at lower temps
2. And the skinnier factor for weight distribution
MUD tires have the flex to release mud so they are somewhat good in snow for that reason, but they are often wide which gets them to float over think hard snow which can be considered at lower temps as ice.
Cheap tires have softer compound, but it is unstable through the temperature range and become very hard in the cold which is why they suck in icy condition.
Higher quality tire have a medium compound that remains stable even at very low temperatures allowing them to keep flexing and also not loosing their adherence on cold icy surfaces. The addition of abrasives in the compound of winter tires is also very helpful to maintain the adherence to the surface.
Thread design and compound quality will influence the noise level the tire will produce. It is actually the edge of the tire that generates the more noise. The sharper the edges the noisier the tire is, which is why AT or Highway tires have a more rounded edge. The more aggressive and sharper edges on MT tires get them to offer better grip on softer or harsher terrain but generate more noise.
For all of these reasons, I DO NOT use 4 seasons on any vehicle I drive. (And that would not change unless I would live in a state Lower than Virginia, or about).
I have good or fair quality tires for summer use and high quality winter specific tires for the winter.
For Winter tires :
On cars and SUV's I have owned Toyo Observe G02+, or Open Country are the ones I have found to offer best traction and road handling in the worst winter conditions. I have tried GoodYear, Michelin, Bridgestone, Coopers, and Dunlop. The Bridgestone Blizzak are as good as the Toyo's but I have found they wear a little faster. The Toyo have walnut shells in the compound, Yokohama's have nylon strands and I have heard they are also good but have never had the opportunity to try them.
Michelin's I have always find were too hard and not as god on ice as the others but work very well in soft and hard snow. The Michelin's however are usually by far quieter tires than the others. GoodYears had great tires in the F32, but they have changed the compound and even though they behave well, they do not fare as well in icy conditions.
For Summer tires :
AT or MT will depend on what you do. if you do not do any Off-Road driving then it becomes strictly a matter of looks. As for which is best it is a matter of budget. If you do a lot of miles, you may want to consider a better quality tire as the stability of the compound can also a factor in rainy conditions. If you only do commuting, low miles and not a lot of towing you can skim a little here and lower the cost to afford better winter shoes if they are required in your area.
Hope this helps your decision making.
