Living in a RV or other type of mobile home is not necessarily camping.
Units adequate for extreme winter weather are available, others can be "beefed up" but a SD winter in any case is going to require utility hookups and a lot of fuel for heating. People convert old buses, mobile homes, RVs and other assorted boxes for use as winter homes in the interior of Alaska. Often the conversion makes them more or less permanent on site, e.g. what started out as a RV is not necessarily a "just hook up and go to the next campground" kind of RV any longer.
A friend in Alaska upgraded a '60s vintage trailer to be more suitable for winter by increasing wall thickness from two inches to six inches, but this cost a lot of space on the interior and made it no longer towable. Others have build around the outside, kind of putting the trailer in a cave. 
In South Dakota, serving the needs of oil field workers in the Willaston Basin fields, you will find RV parking spaces inside heated buildings. That's not a bad solution, if you would like to continue using the RV as a RV when the job is over and you move on to another location.
Rather than convert something, my RV choice for living in that climate would be a small to medium size well-insulated molded shell travel trailer, like a Bigfoot 2500 series or maybe an Oliver. You still need power, and a big tank of propane, to keep the furnace going. Working out how to dump waste water will also be interesting. The tanks can be enclosed, but you still need a line out to a sewer connection that is going to be in frozen ground for the first six to ten feet of soil depth. Mobile homes will sit over this utility space and heat it, RVs are not designed to do that.