Keep in mind that an RV is build for outside:)
Yes, it's nicer if you can keep it covered, and I'd highly recommend that you at the very least, get the tire covers, to help reduce the UV deterioration of the tires.
Will that local place allow you to plug in, to keep batteries charged? It's still a good idea to visit it monthly, to run the genset. Bring along a 1500w space heater, to put a load on the genset, to "exercise" it. If they don't have an outlet you can use (20A would be fine), you can charge the batteries when you run the genset every few weeks.:)
I'd also suggest that if you have a heavy wet snowfall, that you try and get the snow off the roof of the RV as soon as you can. It would help to take the load off the tires (snow gets heavy), and help to keep reduce any damage from melting/freezing snow/ice on the roof....but don't lose sleep over it, if you happen to have a blizzard, and you can't get to it.
As far as being there in the winter....as long as you winterize it properly, it shouldn't be any problem. I imagine you'll see lots of other RVs stored there during the winter too.
You may want to consult some CGs for storage, but you would probably feel more comfortable with a security gate protecting the RV....though that in itself isn't a guarantee. :(
Some (not all) CGs will offer long term storage rates. You'd have to call and see what they charge, and what they offer (will they allow the RV to be plugged in to keep the batteries charged?).
Storing it down south and visiting it is not a bad idea, but are you going to use it as much as you'd want. Would the plan be to take a Fall trip down south, and drop it off, then fly (or rent/tow a car) home until you want to take the next trip? You may miss out on some nice weather trips in the Spring?
Lots of people are doing just what you plan to do, so I'm sure there will be a wealth of information.
We are fortunate that we can park (and plug in) our MH on the side of our house.
The closer the RV is to your house, the more you'll use it, or visit it, and that is good for both YOU and the RV:)