I work and camp full time at White Pass ski area in Washington during the entire winter. Periodically the WSP will hangout at the pass pulling vehicles over if improperly chained. The 18 wheelers are the ones I see pulled over the most and I know of one truck that was fined $400 and some dollars. Most of the time when chains are required the sign will say except four wheel drive, however, there are times when all vehicles must have chains on. No exceptions!
During the winter all vehicles are required to carry chains or cables in the passes.
I know about the 10,000 lbs and over rule of carrying 2 sets of chains and my truck is rated at 12,000 lbs, but I only carry one set of chains though. I go down and back up once a week and haven't had an issue yet.
With all the new deicers (salt) the WSDOT uses in the passes now chains aren't required as often as they used to be.
