Never made a mark on them. Main thing is, don't go too fast, they say max 40mph. In my experience, it's more like 10mph. If you can do 40, you don't need them on......
I could imagine spinning the wheels would cause the chain to damage the tyre, especially if the wheel spun in the chain. But if that is happening, they're not fitted properly.
I usually run the tyres at around 45psi. I found letting them down to 35 gave a better ride with the chains on, and more grip with them off, just had to put up with the slightly wobbly feel when back on tarmac. What will kill the chains is running them on tarmac, they really don't like that, and I don't expect the tyres do either.
It is a bit of a pain, when the road is only semi covered in snow, too much to get up the hills without them, but not enough on the flats.
Car chains would just fold up on a transit, gotta be at least the lightest of the heavy duty ones.
There are some fantastic ones about. The trouble is, its a big jump between the just about adequate £100 ones, and the next step up, which seems to be about the £250 mark. I'd love a pair of them, but can hardly justify it.
These are the ones I had
http://www.snowchains.com/4x4-snow-chains/polar-16mmFive year guarantee with these
http://www.snowchains.com/4x4-snow-chains/ziptransportThis is a brilliant idea
http://www.snowchains.com/snow-shoe-spikes/shoe-spikes-largeTo be honest, I'm surprised how the prices have dropped, and the options increased since I bought mine