Chris,
If Caltrans/CHP has full chain controls in effect due to a storm, they will require you to chain the trailer as well as the truck. They have check stations and will not let you pass if not per their requirements. They seem to put the "chains required" signs up as soon as there is an inch or so of snow on the road. Always seems to be a little early but once you see how some people drive in the snow and ice, I can see why they do it this way. We have WellsCargo construction trailers that the guys have to chain up every once in a while, hear lots of grumbling from them but they have no choice.
Stan