My reply only appies to Colorado and Wyoming since I have lived and we work in this area since 1958.
Colorado only requires chains on semis/commercial trucks Fall through Spring over the mountain highways (The Colorado Chain Law). Lighter trucks, RV's, cara, etc., are not required by law to have chains but it is highly recommended that they have and use chains or proper Snow Tires. If you do cause a traffic stoppage in the Mountains in Winter, and do not have adequate snow tires and/or chains, you are subject to citation and heavy fines plus towing expense here in Colorado.
It is a good idea to have and use chains when needed. For those of us who live year around in Colorado, many of us put winter tires on our light trucks and cars in the Fall and put All-Weather tires on in the Spring. All-Weather Tires are not winter tires, and don't think that they are. All Weather Tires will not save you if you get into slippery conditions in the Mountains. The Colorado Highway Patrol will cite you if you cause a traffic stoppage on slick highways with only All Weather Tires but not Winter Tires or chains.
For anyone traveling I-70, US-50, US-160 and adjoining roads in Colorado, plus I-80 in Wyoming, wintertime weather forecasts should determine travel for anyone not used to traveling in the Mountains in Winter. My recomendation, and what we do living here, it avoid travel over the Continental Divide during any storm when possible, even with chains. Our Commercial trucks, that I own, must travel on schedule so all of our heavy truck have Auto Chains, as do School buses, plus most commercial trucks that travel daily here. Other heavy trucks from out of state use normal truck chains as required.
Also, anyone, resident or visitor, should avoid traveling I-70 on Sunday evening and nights between Denver and Vail, Colorado, in ski season, no matter what the weather happens to be. And, absolutely, do not travel between Vail and Denver Sunday evenings anytime during or a snow storm. If you do, you will be sorry.
When the Colorado and/Wyoming highway Departments have their warnings out on their numerous signs and broadcasts, I recommend that anyone pay attention. In Colorado and Wyoming Call 511 on your phone to get the road conditions. If you are not on a tight schedule, it is recommended that a comfortable stop-over before getting into a storm in the mountains is much safer than braving un-drivable conditions. If you are on a really tight schedule, when the chain law is in effect, either stop before proceding for a few hours, have real winter tires, with studs, or have chains available because you will probably need them. And when the highway is actually closed, (fairly often in Wyoming) then you have no choice.