For me (before I purchased a place with an RV garage) the best solution was to plug into shore power. A 15-20 Amp breaker on a good extension cord will do just fine.
I turned off all the inside breakers for the TV/Entertainment Systems and let it rest for the winter.
Check the charge rate at the batteries once plugged in. You should see 13.4 - 13.7 VDC max. Anything higher will result in the batteries gassing excessive and using a lot of water. You can also add Mineral Oil to each battery cell. (There is a few threads on this subject in this forum). Personally, without the oil, I only top up the Electrolyte once or maybe twice a year. Fully charged batteries will not freeze.
Next thing to pay attention to is Mice. Make sure ALL Food is removed from the coach. If they can smell it, they WILL come and get it. Crawl under and make sure there are no holes where they can enter. Plug the holes with Steel Wool and Spray Insulation. They don't like to chew on Steel Wool.
Of course the obvious winterizing must be done to ensure things don't freeze and bust. Take your time and be sure you have Pink Antifreeze through all systems. Don't forget the Washer if you have one and the Outside Shower Head.
As far as moving the rig. I don't think it is necessary. I parked on pieces of 2 X 12 and make sure the tires are covered from the elements.
Some say to exercise the generator at least a couple times during the winter. I did not but it can't hurt. Give it an oil change and service in any case.
As far as running the Engine, No. You will do more harm than good by starting it up and running without reaching full operating temperature. Just make sure the Fuel Tank is full to reduce condensation and put in an additive as recommended by your local Diesel Shop to keep the fuel fresh. Also, have the coach serviced before you put it away. Crankcase oil becomes Acidic so you want to make sure to have fresh stuff during storage. Come Spring, you are ready to roll....
I used a cover the last two years. Some swear by them and some at them. Me I felt it was worth the hassle because it kept the rig as clean as when I put it to bed and protects from the elements.
Well, there you have my full novel on the subject. It worked good for me.