A tire dealer may have chains available depending upon where you are. You may literally have to drive someplace where chains are legal. IIRC Wisconsin and a few other midwest states metal traction devices, be them chains or studs are illegal. You may not be able to buy them any where! If in the NW and some other western states Les Schwab is probably one of the best or better places to go to. They will setup, show you how to install etc.
I'm not going to say towing in snow is fun, horrible etc. I used to use my TT as a ski hut. THere were many times over 100 rvs of ALL types, sizes and shapes at the local ski area's I went to. We all arrived and left in good shape, got home, and came back the following week from December to early April. Traction tires for the rear of the truck are good. as are AT or equal on the front of the truck, and something somewhat aggressive for the trailer are good too. A 5 rib hwy tire is not as good as something with major grooves on the side. This lets slush etc get squished out as you drive.
There are some vent covers, forget the name. Invest in these for the vents. You can keep the vents open when it is raining and snowing.
keep your water tank full, hopefully it is heated or somewhere with in the heated part of the trailer as mine was. You may get froze out of some area's if you have manual drains. The water will freeze upwards, stopping water from flowing to parts of the unit. Find and remove this drains, then water will flow throw out. If the black tank is fluid, somewhat full, and you have a chance to drain it, do so! 48 hrs of sub freezing temps will net you a chocolate fudgecicle in that tank. possibly to never drain until you have 48-72 hrs of above freezing temps. Unless you have a heated tank.....
As noted, many have said chain up rules. Look up the states that you will travel thru to figure out snow/winter weather rules. In Washington, if you are towing or over 10K lbs total gvw, you need chains for truck and trailer if applicable from Nov1 to April 1. Sometimes the later date will get extended depending upon the weather in early april in mtn passes.
As noted, go per weather forecasts etc. Winter has a different look and feel than summer sunny weather no matter where you are. Hence different beauty to the region(s) you will travel in. You may not also get to places in winter, that you can not in the winter. many parts of Yellowstone, North cascade hwy 20 in northern washington state......
Have fun
Marty