I had similar situation last year wanting to add traction to my Cub Cadet GT 3200 to use with a Snow Blower.
The Blower is heavy and hangs out the front, making the tractor very light in the rear.
I put on 25 x 10 -12 ATV tires and they were a big improvement. I use them year round and do not find that they tear up the yard, but provide a LOT more traction. I have a fairly steep hill that I mow. Probably about 40' top to bottom and the slope is steeper in some areas than others. I mow up the steeper parts(weight transfer gives rear tires more traction) and down the areas with less slope. With Turf tires, depending on the amount of moisture I could sometimes go down most parts of the slope without sliding, but if moisture was presents it would usually start sliding about 1/3-1/2 way down and then the tractor would pick up speed and get to the bottom of the hill usually going over 10 MPH. Tractor has power steering so I can control it, but it still is not safe and I do not let others drive the tractor on the slope.
With the ATV tires(and no weight) I can usually go down the slope, even if the grass is slightly wet. At times it will still slip a little, but does NOT go into a seemingly unrestrained slide down the hill, it just scuffs the turf a little, but still maintains a lot of traction.
I also have a set of AG tires and they did not perform much different than the turf tires on the hill or in snow.
The ATV tires have MUCH better traction than the turfs or Ags in all conditions I have tried them in
For snow use, with the Snow Blower I needed some ballast, even with the ATV tires. I have countered a bunch of weight hanging off the front, by hanging weight off the back and IMO this is the most effective way to get traction.
I decided to build a bracket to hang out the back, but when I started building it, I was not sure what I was going to use for weight.
I did not want to spend a bunch of money so I tried to use things I had on hand. I had some 3" x 3/8" steel that I bolted to inside of the frame rails where it is very securely attach and easy to detach and reset.
When I got to the point of putting something in the back to hold the weight, I got looking around and found that I had some scraps of heavy wall pipe, but did not think it would be convenient to hang weight from the pipe.
Then by coincidence, I move the Loaded Turf tires that I had previously taken of and the thought occurred to me that they would make pretty good weights(probably 60-70 lbs each) and I looked at how hard it would be to attach those.
It was a bit more work than just welding something on, but I ended up cutting 2 larger pieces of pipe(IIRC 2") and slide them over ends of (IIRC 1.5" pipes) I made some flanges to attach to the wheels and welded to the 2" pipes and used a piece of threaded rod to hold them onto the 1.5" pipe.
With it all assembled the Wheels/tires act as WHEELIE BARS since they can rotate on the pipe. With over 150 lbs hanging more than out the back, I have used the Wheelie Bar function a few times when playing around with the Snow Blower off.
With the combination of my Wheelie Bar Weight and ATV tires I got VERY good traction with the Snow Blower. Only issue I encountered was the added length of the tractor and I found that in snow over 1 foot deep the Wheelie Bar Tires would encounter snow resistance when backing up in a confined area.
This year I bought another GT 3200 that has a Power Angle Plow on it. I plan to make a similar weight rack for the back of it, but the new plan is to use to a barbell and steel weights that I bought over the summer. Should be more compact, but function pretty much the same and will even have a Wheelie Bar function with the barbell and weight.
