As snow plow driver who has frequently pulled trailers of all types in poor weather situations ...
The keys to driving on slick roads (with trailer or without) is GO SLOW, PLAN WAY AHEAD, and unfortunately WATCH OUT FOR THE OTHER GUY. If you are driving slowly and you loose traction, you will have time to react and if you do loose control the damage will be minimal. Regrettably, there are many out there who believe that their Mega 4WD SUV and super snow/mud gripper tires make them impervious to the dangers of slick roadways. These are the idiots that cause lots of damage and hurt people. Watch out for them and stay as far away as possible. No offence, but this includes some small AWD car owners as well. For some reason, while they are very good little cars, they aren't impossible to wreck and the enhanced ability to GO doesn't mean that they have an enhanced ability to STOP.
Once things begin to slide with a trailer, you're just along for the ride. The trick is to never get in the situation where you can loose traction. With a trailer, and the inherent joint in the vehicle, you don't have to actually hit anything or leave the road to do a lot of damage. A simple jackknife can ruin your day. Look farther ahead than you normally would and make all speed and steering adjustments slowly and deliberately. Pay attention to what the trailer is doing behind you. In slick conditions, very light trailers (like teardrops) can slide long before the tow vehicle does. Know how to properly use and adjust your trailer brake controller if you have brakes and adjust it often for changing conditions. Locked wheels will give you zero steering capability and on a trailer will jackknife you VERY quickly. Be aware of drifting snow. Snow drifts are often difficult to see and can be just as bad as leaving the road in smaller vehicles. Also, remember that ice can be visually invisible so be aware of the possibility of encountering ice at all times. I have seen layers of frost that looked like a dry road and piled up dozens of vehicles. You can also encounter slick conditions out of season. A liberal scattering of 1/4" hail stones from a high elevation mid-summer storm can be just as treacherous as a January ice storm.
Snow removal and de-icing policies and techniques vary dramatically as you travel across the country. Be aware of those policies in the areas that you travel. It will help you make good decisions. Please be considerate of snow removal crews who are trying to clean up parking lots and roadways. If you encounter a working snow plow, rest assured that conditions behind them are better than ahead of them. They may be slow, but they are doing their best to improve conditions for you. On two lane highways, please don't pass them. Stay well back as they are often scattering de-icing agents and grit on the roads. Be aware that in most situations they have a specific area of responsibility and will stop, turn around, work across the center yellow line at times, drive along the shoulder, and all other types of unusual driving behavior. Give them room, and expect the unexpected.
In my opinion, the best advice is to find a safe place to stay put until the roads have been cleaned up. In many places (freeways and most highways) cleanup only takes a few hours after the snow has stopped falling. If you have found a spot to wait and see them working, make sure that you aren't in their way. The snow and sand/salt/chemicals that they throw can and will cause damage to your vehicle, give them ten feet or more to get past you. When possible, move your rig to an area that they've already cleaned, preferably away from the edges or any piles (they may be planning on a final pass around the edge or adding additional snow to a pile.) If you are in an unlit area, turn on your hazard lights (NOT park lights) to help others see you. The danger of park lights along a roadway is that in poor visibility traffic will sometimes "follow" a parked car and cause an accident.
Also, remember that the roads are slickest at temperatures rather close to freezing (20°F to 35°F). Very cold conditions are actually easier to drive in than slushy, wet conditions.
Please be careful out there. Winter can be a wonderful time to enjoy the outdoors, but it can be dangerous and even deadly if you are unprepared for the challenges that cold weather produces.