If you use them properly, they shouldn't cause damage.
- Install them tight, get some good bunji cords or factory tightners to keep them tight and have a couple of spares. If the chains are operated loose they will hit things as the centrifugal force spins them outwards.
- Don't run them for long distances on dry pavement. Besides wearing them out, the cross members will break and tear up anything within reach.
- Don't run them for long distances on hard ice or dry pavement. The chains should sink into the snow covered pavement. I've seen tires where people ran the chains way too long on the chain cross members wore slots into the tires ruining them. Lazy driver with a lighter wallet.......
- For easier installation, assuming you have rear duals, get two pieces of 2X4 or 2X6 about 8" long. These are to run the inside dual up on. This will lift the outside dual off of the ground sufficient distance to slide the chains under the tire and then provide room to work them around to get them tight.
If you just need them for one trip, I have seen auto part stores in ski areas that sell chains and then if they're unused, they'll buy them back for about 50% of what you paid for them. That's steep, but if you're never going to need them again.......
I've never used cable "chains" so I can't speak about them.
Bill