Seems like every fall we have people asking if lug tires eliminate the need for tire chains. I guess it's a valid question, but when you're pushing snow I can't say I've EVER had too much traction. Front mounted blades and especially snow blowers transfer weight off the rear tires onto the front tires and reduce traction. You need added weight plus something that will increase the traction on slick ice & snow covered surfaces.
I made the comment a day or so ago about HDAP tires being better than turf or lug tires. Plus most 4-wheelers seem to push snow a WHOLE lot better than garden tractors do, but lots of those are 4WD, but I think the tires have a lot to do with it too. Softer rubber compounds of ATV tires grip snow/ice better than the hard rubber used to mold the lugs on lug or turf tires.
My family has had many sets of Bridgestone BLIZZAK tires for running on snow & ice. I bought a pair of Firestone Winterforce tires (same tread design as a Blizzak but molded from slightly harder rubber for longer life running on dry pavement, gives up a bit of ice traction, same traction on snow, and much longer tread life) for my FWD car in the fall before we had over 100 inches of snow several years ago. I was AMAZED how well they got me around in snow. They compress and grip the snow with thousands of sipes, and really make you go as well as AWD or 4WD. The only days I used my 4WD truck was when the snow accumulation was predicted to be well in excess of the ground clearance of my car. The most memorable day we had 15-17 inches. I even buried my truck in my driveway getting off the road that night. I think someone should mount up a pair of Blizzaks on a Cub Cadet and see how they compare to chains on turf tires. I don't think they would out-perform chains but they may come close to the same performance.
Anyhow, with light snow accumulations, 1 to 3-4 inches you may get along on grass or crushed rock with lugged tires O-K, until something causes you to slip a tire.If there's a layer of compacted snow or ice then you won't be able to move. Then you're stuck! The snow compresses, forms ice, and you have NO traction. Chains would allow you to eventually get out of the situation. This is true on 700-1000 pound Cub Cadets or 7000 pound farm tractors. One day we had the M sitting on a layer of snow/ice maybe 1/8th inch thick spinning both rear wheels and it wouldn't move. It was on a side slope, not going uphill or downhill. Typically with a car/truck you can increase wheel/tire speed to create enough friction heat to melt the snow/ice but that's not really possible with the slow speeds a CC or FARMALL runs.
If you have fancy stamped concrete, or cobblestone paving, or blacktop, and don't want to use chains because it may scratch or damage your pavement, I guess there's always a broom and plastic snow shovel you can use.
It's been my experance that Firestone tires last longer than other brands, and also pull better in most conditions. They still advertise they're "Gum-Dipped", not sure what that exactly means but I have some suspicions, and they do resist cracking & weather-checking much longer than other brands, especially the cheap imported tires. I've had several Good Year tires crack & check bad enough they ripped the sidewalls out or split the casing down the center of the circumference of the tire. The Firestone tires Miller Tire sells are not made by Firestone, Miller has licensed and modified the molds and has them made by other companies, some located off-shore I believe. Not sure they add the expense of Gum Dipping them. But Miller is a very reputable company with great customer service and I think they would sell a decent tire and stand behind it.