I know all too well about Iowa winters. I winterize vehicles for friends and family etc and one has 20's and another 22's. The way i clean, Prep and wax them is simple and actually lasts.
Start by soap and water wash. Then get never dull, Straggly cotton type stuff and go over them a few times with that. It will get dark spots and any other imperfection off. Then i apply a couple coats of eagle nano wheel polish/wax. It leaves a good wax film that mud, Salt, Brake dust can be wiped off with a damp towel or shammy with no water spots or streaks.
I use a couple terry cloths and a few micro fiber rags, Micros from wash on. It takes some time the first time around but after you get a good coat on them, Its easy to keep up. What i usually did was have my buddy swap off the 22's and drop them off. I bring them inside and do a wheel at a time watching TV etc. Makes it easier and also flys by.
He would DD it and wouldn't bring it back until spring for fluid changes, Detailing etc and the wheels always looked good and still had a good coat of wax. But it all depends on if he actually keeps up with his wheels and wants them to remain mirrors. If hes committed to it they will look new every time. Good luck
Couple TJ's and a XJ