I may regret this....I have a TC35D and I run front only chains....now before you attack, wait for the explaination.
The Class III Boomers are indeed capable of great traction due to their weight and such, but I find I need a bit on grip up front to aid in steering and slide control. That said, I only run the chains when needed, and only on my gravel drive and in the fields crossing to the drive from the 'garage'.
I feel that if you use some common sense, and don't try to bully the snow, the chains won't do any damage. As stated, I use the chains more for steering control and don't use them as a traction aid to push huge piles or climb ice walls. I had found that when pushing with the plow angled a bit, especially on hardpack or ice, the tractor wanted to crab sideways. The chains definitely help here.
In addition. when coming out of storage 'garage', the chains sure help crossing the field, hardpack, and drifts.
I probably run less than 20 hours in the winter with chains...all slow and careful operation. No problems yet.