Knowing where you live, obviously you have it winterized.
I would leave it that way while traveling. Consider the use of a porta potty for those "unscheduled" stops.
Once you get where you have full hookups. You could use electric space heaters and only use the furnace periodically to prevent holding tank freeze.
The grey water with full hookups is not an issue. As you can keep the dump valve open. BW however is another story.
We just returned from a trip to So. California. Via Raton Pass in both directions. Spent 3 unscheduled nights at the Pueblo south KOA in what amounted to a foot of snow on the trip south. Then 5 unscheduled nights near Socorro, NM on the return trip. Waiting for the snow and ice to be cleared on I 25 between Albuquerque and Colorado City.
I de winterized once we got far enough south. Then winterized again before leaving Socorro, NM.
Running the furnace while traveling will use an enormous amount of propane. When you stop, use space heaters and the furnace to warm the cabin up quickly.
During the trip in the cold country. I used RV antifreeze to flush the toilet. But no solids or toilet paper were put in the toilet.
We travelled in temps as low as +8 F.
While the BW dump valve was froze enough to where I didn't want to force it open. About 5 minutes with a hair drier and it worked freely. The waste water ran right out. But it was slushy.
We did use city water in NM but had to disconnect the hose before going to bed to keep the faucet and hose from freezing. In places where it was too cold to use city water, we used the onboard tank. But did not flush the toilet with fresh water, only RV antifreeze. At less than $3 a gallon it was worth it not to have frozen and perhaps damaged holding tanks.
Good Luck on your trip.
As you are probably aware, most states have websites for road conditions. ie www.cotrip.org
Many have web cams on the major hiways.