Again, I'm from AZ, so what do I know... but I don't understand why we're talking about carrying chains in order to pull a trailer across the southern tier of states in winter.
Let's say you hit snow, or worse, ice. You put on chains and keep going. Unless you put them on the trailer, too (can't imagine what that would do to a fiberglass trailer)... what's going to happen when you hit the brakes
? Won't the trailer have a tendency to want to pass the tug?
I do actually have experience in winter driving conditions. I lived for a number of years in a high altitude town and my daily commute involved 20 miles of twisty mountain grades that were frequently snow covered. I have used chains. I loved my Subaru. But not with a travel trailer.
I do know there are some who like to use their trailers in winter conditions. I know some live where snow remains on the roads for months at a time and may have to do a bit of winter towing just to get out of Dodge. Y'all can do what you need to do. But I think the OP can get to CA without chaining up, and I think it would be better that way.
Storms can happen, both on the way out of the northeast, and while traveling west even in the southern states. When they come, you follow the forecasts, find a nice campground, plug in the power, turn on the furnace
, and wait for the roads to clear. My mother has made numerous winter cross-country trips in her motorhome without ever having to carry chains. On the way home last February, she did have to stop over in SC for a couple of days to let an ice storm pass through.