Fall is the best time to camp all year. Go use it
Most people put the camper away too early, out of habit rather than because of the weather.
Fall is the best time for camping in Ohio, and it is not close. The bugs are gone. The campgrounds that were impossible to book in July have openings midweek. Nights are cool enough that the furnace is pleasant instead of necessary, days are warm enough to be outside all of them, and the trees do the thing you drive to other states to look at. Rates soften after Labor Day. The people still out there tend to be the ones who actually like camping.
If the camper is sitting in the driveway right now, that is a decision you are making by not making it.
What changes about a fall trip
Not much, and the small things are worth knowing.
You will use the furnace. Which means you will find out whether it works, how loud it is at three in the morning, and whether the propane is where you thought it was. That is useful information to acquire on a weekend you planned, rather than on the first cold night of a trip you did not.
Days get shorter faster than they feel like they should. Setting up in the dark is a different job from setting up at six. Give yourself a bigger margin than summer taught you to.
Water is the one thing that changes the calculus. A hard freeze overnight can reach the lines in an unheated bay, and late-season trips in Ohio can get a cold snap well before the average first freeze date. If a low near freezing shows up in the forecast, you either keep some heat on or run with the tank drained and jugs aboard.
That last one is the bridge to the rest of this.
Your last trip is your best diagnostic
This is the part almost nobody takes advantage of.
On your final trip of the year, you are running every system at once: water, pump, water heater, furnace, fridge, awning, leveling, all of it. That is the only time all year when you will find out what is not right, at a moment when you can still do something about it.
So take a notebook, or a phone, and write down anything that behaved oddly. The faucet that stutters. The slide that hesitated. The seam you noticed on the roof while you were up there with the cover. None of it needs to be solved on the trip. It needs to be recorded, because in April you will remember that something was wrong, but not what.
When to actually close it up, and it is not a date
Here is the thing worth carrying away.
Winterizing is a forecast decision, not a calendar decision. The average first freeze in Columbus is in the back half of October, most years between the 23rd and the 27th, but averages are not promises, and the cold does not consult them. Plenty of Octobers have delivered a hard night ten days early.
So the answer to "when do I winterize" is: before the first hard freeze appears in the forecast, not after. Which in practice means being ready to do it on a few days' notice from about the start of October, rather than having it booked for a specific Saturday and hoping.
Waiting until freezing temperatures are already in the forecast is where the risk comes from. Not because the job is long, but because that is exactly the week everyone else has the same idea, the storage yard fills, and the one shop in town that does it stops answering the phone.
The two decisions worth making now, while you are still out enjoying it, are where it will spend the winter and who will do the work. Both get harder to answer in October.
Then use it again
Go camping in September. Go again in October if the weather holds. The close-up will take an afternoon whenever you decide to do it, and the list will be shorter if you write down what you notice while you're out there.
That is what goFrigg is for. Everything you own gets its own checklist; what you notice on the last trip is added to it, and next spring you open the list instead of trying to remember.