I try to avoid it as much as possible. Driving in icy, snowy weather is hard enough without anything behind me at times.
I've been caught in one freak snow storm years ago in May. Drove slowly and cautiously. Visibility was horrible as well. Stopped at every small town to have a break and clear snow and ice off.
Oddly enough though, the added weight in the rear due to the trailer seemed to give me more traction.
We've had to camp out in our trailer as early as late March and late as early November here in Canada due to certain circumstances, not just vacationing and we've been able to miss bad weather those times. Days were warm but the nights are chilly so be prepared to use sleeping bags and heaters. Don't put water in the lines in the trailer until you can keep it consistently warm.
If you really have to do this, I'd watch the weather and wait until late morning to get going. Let the road crews clear out the roads and let the sun melt off any ice and stuff. Wait until the weather breaks to travel. Avoid freezing rain, blowing snow types of situations and be ready to camp out in a hotel/motel in communities on the way to your destination.