There was a long term campground near my university years ago. Viable sounding option. But, the few miles journey between school and camper would have been a bugger on nasty weather days. Bicycles are fine when it's warm and sunny, not so nice in freezing drizzle and such.
A trailer instead of an RV, where you leave the trailer there and drive the tow vehicle to class might be a better foul weather choice/thought.
Keeping the interior of an RV or trailer from freezing isn't that hard with enough BTU's. But, keeping a water tank that's hanging down below away from heat from freezing, that can be an adventure I'm sure.
Not at all sure how the Walmart thing works, but I know it does. There are campers that have been at our local Walmart for years now. As in many years. Guess they potty in the Walmart, but I've no idea how bathing works.
I know you said you've got places to stay worked out. But beware of complaining neighbors. Many won't object to a visiting RV showing up on the neighbors yard for a weekend, but after a week, they may start calling in complaints, which can create headaches.
Just a few random ruminations.