Wisconsin Adventure...

We used a 110 plug in at my brothers and got along fine. We are a 50 amp motorhome. We just used propane for the water heater and frig. Didn't need heat, but could have used A/C. Instead we used the ceiling fans with windows open and had a floor fan rotating- moving air seems cooler. In your case you can use your furnace for heat. Just be mindful to not use many thing at once.
As far as filling propane, do a google search when you get there, or you could do a tank exchange if you use 20# tanks. If an onboard tank you can do an extend a stay and then use the 20# tanks which are easy to refill/exchange. Many grocery stores, hardwares etc have that. Some gas stations have propane fill as well as farm coops. Or, if you drive by a large propane dealer they usually will fill for you. Many of the Flying J truckstops have on board tank fills available.

We just stayed in my parents driveway in Racine early in March. We plugged into their electric with a reducer and just used the lights and propane for heat.. There is propane at Burlington RV at the Racine, hwy 20 exit.

Any propane business should be able to take care of that worry.

Also, some Menards home center stores have vehicle propane dispeners in the parking lots.

You might want to check to see if the nearest Menards has propane. They recently added the service of refilling tanks.
I've never stayed there, but Chain of Lakes State Park in northern Illinois might be open. It's about 30 minutes from Lake Geneva.

Agreed on Chain o' Lakes. It was open in late March in 2011 (when we stayed there for a night.) No water, but the pit toilets were open, and so was the dump station. Electric hookups (30 amp available; possibly 50? haven't been to that CG in 6 years.)

Did you 'call' any of them? Ya their websites will state when they open for spring etc. but most stay open all year.

Almost all of the CG's are open but the water is not turned on. You will have electric and dump hookup. Most have bathrooms that are heated so they leave the water on in them. you can shower there. It's best just to pull in these CG's and they will let you stay. If you call they'll say they are not open.

Call Coachman's in Lake Geneva. Small but nice and Lake Geneva is just down from it. If you look it up on line it will look like a mobile home park. But there is a section in the middle that is for RV campers.

I stayed there every summer when I was traveling! :C

Not close but open. Just go up RT. 47 once parked. At this time of the year they put me in a pull through. Off of I90.
http://www.lehmanrv.com/