Lot to read at their site, but by glossing over it, it seems that they can handle those low temps. I question 'testimonials', as I wonder it they are real. However at this site I would weigh-in that they are real, and many are in extreme cold areas of the Continent. Without going back to the site, I seem to recall that it is suggested to travel at low speeds, (30mph), as they can't claim higher speeds due to some politically-correct insurance thing.., sheesh.
As for damage; from "ROCKS".., lol, they offer a rather complete three year warranty.., as I recall. I wonder about that too. As for construction; I am not certain, but from what I think I see there would be no metals in the cross-over 'X' pattern centered on the tread's foot-print.
For sure, chains in deep snow with rocks exposed might be the better application. However different geo-areas might not be so damaging. My area does not have sharp rocks, mostly frozen mud/tundra stuff, and rounded rocks/small boulders, etc.
As a slight aside; I have traveled through pre-existing rtv tracks on my Yamaha Kodiak 400 where previous warmer season 'balls-to-the-wall' dudes have unnecessarily torn up, and uprooted rocks, roots, and dug deeply down into the turf from their extreme tire lugs making egress even more difficult for negotiating same at a calmer pace with less aggressive tires. I tend to avoid those areas when the big freeze comes, and snow hides those tire-piercing/slashing-objects.., chains, or no.
I use Blizzak winter tires which are siped big time. In fact they are used on a frozen lake in automotive racing, and are generally superior to studs. My use is for normal bad condition highway travel whether ice, or snow, or both.
I doubt those agencies that 'mandate' chain-use over mountain passes in the lower 48 would let me pass by.., even with such superior tires. (However we in Alaska do not have those safety advisories standing in our way. THEY just close the road off from travelers). Whatever.., It's smart to have either chains, or those snow-claws, or some-such, available in a pinch at the very least, or for longer prolonged slower speed driving.., should one intentionally want to.
Once went off of a dirt road with only a clear sheet of solid sun warmed wet flat ice on it, and lost steering control. Not because of the Blizzak tires, but when my 100 pound dog landed on my lap barking, and gnashing the door window charging a moose.., sheesh. Left rear wheel ended some three feet in the air, and all others down deep into the snow, and with no traction available beneath. Placing chains, after the fact, would have impossible for me to accomplish in that situation. However those 'claws' would have been easy to put on according to the site's blurbs, (especially since I carry a small shovel on a rifle-rack), and I would not have had to find assistance to be 'rope/towed' back up, (in a back country area), onto the road. In this, (lol.., off-road), example I think the 'claws' would have been the superior option.
Still I hope that some

member has experiences with the claws to chime in the pluses, or minuses as per.