Your trailer will require at least one wheel have chains or cables applied so the trailer brakes will have some bite if there are chain up requirements. Whether your vehicle is 2wd or 4wd, you will need to chain up the rear wheels if restrictions are in place. You may find chain requirements are only for vehicles above a certain weight or that are towing - Do not assume that because the vehicle next to you does not have chains, that you do not need to run them. My 4wd F250 could be run without chains as long as I did not tow - My 4wd 5500 requires chains even when not towing due to its weight. I would advise waiting out storms where chains are required but still carry them just in case you are caught somewhere that required them to get out of even worse weather that may be approaching.
I run my furnace in the RV when traveling in bellow freezing temperatures. Others will drain and blow out their lines to prevent freezing. Remember that any fluids in containers will also freeze in your RV if you do not run heat, so remove them or carry them in your tow vehicle.