I'm probably adding to the confusion but here goes.
We took a trip to AZ the first week of Jan. Our RV was already winterized but we could not trust filling with water until we got to AZ due to really cold conditions. Right now, very cold weather seems to be existing in the Midwest and Northeast so I would be very concerned with traveling unwinterized.
I just blow out the lines after draining the fresh water and water heater tanks. At home I have a compressor to blow the lines. On the road, just go to a service station or truck stop and feed quarters into the machine. I always leave the faucets open (and don't forget the outside shower) to allow escape of any pressure caused by freezing, just as an extra measure. Use a gallon of red stuff to pour into the traps and any extra into the gray and black tanks. Learning to blow out your tanks is the only way to travel confidently in the winter. Total cost will be less than $10.
Living on bottled water is a lot easier than paying for broken pipes. Just be sure to add some windshield or pink antifreeze to the gray and black tanks as you put liquids into them.
If you have to pay for a winterization, have the technician show you what must be done for a blow out so you can handle the problem in the future.