I agree - an extended-stay motel would probably be your best bet. Very, VERY few CGs stay open in the winter. Not sure any in that area stay open year-round. Illinois winters are not to be taken lightly.
We stayed in our TT in late March one year - temps below freezing at night, snowing one day - and went through 2 30-lb tanks and 1 20-lb tank of propane during that 10-day period. And this was a TT with enclosed belly and under-floor ducting. We also used (and still do, during shoulder seasons) a small electric space heater to supplement the furnace.
Just a quick check of Dixon and Rochelle (both about 20 miles from tiny Ashton) show several chains - Comfort & Quality Inns, Holiday Inn Express, Super 8, etc. - in those towns, plus others probably available in DeKalb (farther east than Rochelle). Some of these may have "efficiency" or suite-type accommodations with a fridge & microwave, as well as longterm rates.
If Illinois state parks are open for camping during this timeframe, there will be no water, either as a hookup (they don't have those anyway) or even in the bathhouse. Likely the only "facilities" will be pit toilets.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
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