We have thousands and thousands of winter driving miles with our TC's over the years.
The weight of the TC does help. We use AT type tires, I have never felt a need for snow tires on the highway with 4WD. We usually have one set of chains available but seldom use them (I hate chains). We have/would use chains to get to a safe haven and shut it down.
We do not do ice, even with one set of chains it doesn't work well. Add a second set of chains and you are a target.
Our camper is just another load. We have virtually no sway. When we had the Lance it was on a dually and we had no problem either. A top heavy camper/truck combo might be another story.
4wd is good for those tough situations, getting going on a hill, going around a stuck vehicle etc. We seldom have the truck locked in 4WD. For us it does not make sense to have the truck in 4WD for hundreds of miles. It really saps the mileage and the speeds will be much lower.
Other traffic is an issue, we will pull off if there is a lot of traffic, that is what will get you in real trouble.
If there is a snow plow up ahead, I will follow it and pace myself with the plow.
Stopping distances are even longer and people love to cut in front of us, life in the slow lane is that way.
We were in the big storm back east in December 2009 and had no problems whatsoever. We were able go where we wanted, when we wanted and frankly there was little traffic.
The most significant effect is that driving in bad weather is a lot more tiring. The solution is to pull over sooner, that's just the way it is. If your too tired to know the difference, then its just too late. Its all about discipline.
We don't think twice about traveling with the TC in the winter. The bigger question is winterization of the TC our heater is on water in the tanks and we get propane every 3 days. Dumping the tanks can be more difficult but it works out.
Good Luck.