There are a lot of variables here that I have not been able to clear for you.
First, is a Jayco Seneca 37HJ listed as a "Four Seasons" unit? If it is, you are pretty well set already. You may have to put a lot of hours on the APU (genset) to run the tank heaters, but that is what that stuff is there to do.
Chains.... You should be able to chain up the outers of the rear and that is all you will need. Hang on to your socks when you go to buy chains. If things are going to be that rough, have chains X4 for the Jeep and a snatch strap. If you are going to carry chains (maybe required for transit in WY and CO) also carry an 8X10 plastic tarp. You can fold it multiple layers thick and use it to lie down to get the chain up done.
Most of the roads have to get cleared for truck traffic, but getting stopped for a day is pretty common. As the coach and handling it is new to you, it is very important that you don't over reach your own capability.
We used to travel in winter a lot. I always put an extra day in the schedule for any winter run and we used it often. My coaches have had the potable tank in the heated space, so water was no an issue, but I don't know that your will be that way.
I hope you have a boring run south.
Matt
