I would absolutely hate to have to chain up the trailer to get out of a camping spot. Why not stay an extra day or two. Or chaining up to get into a spot, why not wait a bit? Or come back for the trailer in a few days?
But I suppose you could get into a situation trying to get over the Siskiyous to get home.
In that case ride quality would be secondary to maximum traction and that means large chain links. It also means chains running diagonal or diamond or whatever to help with sideways slipping. But, there's not a lot of clearance, so I don't know how much you can get away with. The whole idea sucks.
I believe, in CA, if you chain up the truck you must chain the trailer too.
I travel the mountains a lot in winter, without trailers, and I never chain up because I have 4WD and always use aggressive tires to avoid the problem. When my father was still working, he would drive a few miles every morning, before dawn, on his way to work. Then stop, remove the rear, chained up snow tires, and install a set of standard tires. Then on the way home, he'd reverse the procedure and get home on the snow tires with chains. The driveway was too steep to drive up, so he'd park at the bottom and walk/slide down every morning in the dark. He did this very day, to and from work in the winter. Yikes.
One morning he was on his way down and slipped. He accidentally threw his keys up into the air while trying to recover. But they didn't come down. After looking for about an hour with a flashlight he got my Mom's set and went on. They later found them stuck in a tree. ????