Recommend you have a google at "tire chain requirements" for each state you will travel in. Some require you to carry chain when towing, or over a certain weight. Pick up a set of at least cable chains for the truck and a light set for one axle of the trailer and carry them with you. Oh, and make sure they fit before you need them :). Chains along are an excellent bad weather repellant.
A couple winters ago we travelled I-15 in snow most of the way from Shelby to east of Hurricane UT in both directions. Snow as in wake up in the a.m. in Fillmore, UT and the snow on the hood of the Dodge is 3/4 as high as the cab roof... snow as in an icy and windy stretch by Fort Hall, Blackfoot, and Idaho Falls so as you can see the lee side of your trailer in the mirror as it dog tracks along on the ice (OMG!). The 5 cars/SUVs that passed us all parked in the rhubarb further up the road. "Those black volcano rocks are hard on the plastic front end of the posh Cadillac", remarked my co-pilot.
We have also made the passage with zero snowfall, staying in our rv overnight the whole way in both directions.
Carry chains, take your time, turn off the drama media radio and enjoy the trip as well as your destination.
Safe travels.