You are pretty much safe on the interstates in the winter if you watch the weather reports. Like mentioned not only snow reports but wind reports which can be dangerous. Black ice can be a real hazard.
Off the interstate in the winter could be a major problem if you are not familar with the area.
We're in the 21st century dial 511. Most states have weather info available on phone. If you have internet many states have DOT info for the truckers that is available.
Wyoming has some of the best weather information available both on the phone 511, or nationwide 888-996-7623. If you have internet
www.wyoroad.info/
The Wyoming web site also lists other states under neighboring states. Wyoming also has a snow plow priority plan. Be familar with it and the maps they show. During a heavy snow storm if you are on a low priority road you may not see a snow plow for a long time. Maybe over a week.
Other than that it is a piece of cake. Like mentioned, tire chains for tow vehicle and tire chains for the braking axle of the TT, or toad if in a MH. I have towed a TT over some of these passes in the winter, just be cautious. I now have a MH. Much more weight to think about. I carry chains for my MH. Cable chains are lighter and are very easy to install on vehicles, especially MHs. I would recommend them over the old style chains. for MHs you can buy bus cable chains.
I blow out my water lines at anything below 10 degrees F. Fill up again when above 10 degrees F.
The big thing is CAUTION and WEATHER REPORTS. Don't get overly brave, stay on the interstates as much as possible and you will be OK. That said I have to get off the interstate at Rock Springs and go north over South Pass to get to Cody (7500 ft). I have driven it hundreds of times in the winter but I still use a lot of caution.