Purefection said:
Studded tire = traction device. Problem solved
It is important to keep in mind state and local laws. In many places, studded tires are either forbidden or only allowed in some extreme conditions - and changing between studded and non-studded will certainly be a pain. Driving studs on cleared pavement can damage the pavement, for one.
Tire chains also have some laws surrounding them which vary by jurisdiction - it's important to read up. Reach out to the local police department on the rules regarding them, they can put it in "practical" context rather than "legalese," and you'll get an idea on what they're more likely to enforce if it's a gray area. They're also easy to remove and install, unlike switching tires.
You can do it to any driven axle, but chains should not be installed on non-driven axles as they can become damaged. So, rear is an obvious choice, with front being optional, though with the way the AWD system works it may be questionable whether the axle should be considered "live enough."
Only one more question... which class chain would the 360 handle? S, U, or W? Probably not W as the manual claims there's clearance issues. Then again, this thing may have been included in the manual to keep people from screwing up their vehicles with faulty use of chains, or as a method to escape warranty claims if snow chains were used (though the tiny 36k warranty didn't go too far anyway).