I think it depends on the road and the conditions. I've seen "Chains or Snow Tires" (i.e. no 4wd required) and I've seen "Chains or 4WD" (no chains required on 4wd). I do believe there is a higher restriction of chains on all vehicles, but I don't know how often that is used.
Only with R5 conditions. Chains and 4WD required. It's not used very often. They are more likely to close the road, but on rare occasion they go with roads being open under R5.