If there is any possibility of being out in snow or icy conditions, cary chains for both the tow vehicle and the trailer. Know how to use them and do use them if the road surface warrants.
Most storms only last a couple of days to a week and most major roads are quickly cleared of snow after a storm. This means that you should find a place to park when the roads are unsafe. Wait it out if at all possible.
Always check for road conditions before heading over passes and check weather forecasts before every leg of the trip. State DOT will have road conditions numbers and web sites. NOAA has weather forecasts. Itis getting so you can also find webcams for most passes and see what the conditions are like.
Do not get in a hurry when conditions deteriorate. If someone wants to pass you, let them. You can then enjoy the show as they try to maintain control on a slick road. Keep the idiots in front of you and not behind you.
Be prepared. Keep all equipment in top notch condition. Be ready to survive a week off the side of the road. Have emergency communications. Know how to signal distress. Know about hypothermia. Know about carbon monoxide and similar dangers. Keep fuel tanks full.
Drive carefully. Do not do anything more than feather the brakes. Avoid any maneuvers - if something gets in front of you drive over it.
And fill the coffee pot before you go to bed so, if it freezes, you can still have hot coffee in the morning.
for some ideas and links on keeping warm.