I've been running dedicated snow tires for about 15 years, and about 10 of them on at least 2 cars (since I met my wife). I've crewed for Rally teams at SnoDrift 6 years, and I've spent hundreds of hours ice racing on numerous tires. They will make a huge difference. Even the cheapest, off-brand, dedicated snow tire will perform better on snow and ice than the best all season.
That said, they're not all equal, some have larger openings between lugs, better for snow (the original Winterforce, or Yokohama A034 competition tire), some have a lot of siping to grip on the ice.
I live out in the country, but very rarely find myself in more than a dusting of snow beyond my driveway, so I'm concerned mostly with ice performance.
Studs and chains are not legal here.
IMHO, Nokian Hakkapeliitta tires cannot be beat. I've owned Qs, Rs, and 2 sets of R2s, and will be buying a set of R3s before this season is out.
Michelin X-Ice and Bridestone Blizzak are close behind. Nokian is a little weird about who can distribute them, so it may take some shopping around, whereas Michelin and Bridestone can be bought just about anywhere.
Beyond that I've used Cooper Weathermaster, Firestone Winterforce, Goodyear UltraGrip Ice, and General Altimax Arctic and been pretty similarly impressed. I also had a set of Falken Eurowinters, and was pretty unimpressed. Still better than an all season, but not much.
I also highly recommend having a separate set of wheels. Not only does it save the cost and wear of mounting and balancing, but the hassle as well. Tire shops up here are booked out for weeks this time of year, so you either have to put your snows on early and run them in warmer temperatures than you should, or drive in the first few snows on your all-seasons. When they first forecast a decent snowfall, I spend an hour or so in the garage the night before swapping the snows onto both our cars. And I can swap them off as soon as temperatures start to warm up, and occasionally have to swap them back if we get a late spring storm.
If you only run them when the ground temperatures are below about 40, they will generally last 30-50k miles.