I've been there and done that. You're more limited at Winchester then at say Florence. But if you air down your tires you'll find they do pretty well. In fact the stock Polaris PXT tires are pretty amazing for the Dunes. I have had them and Big Horns on mine, loved the BH but the PXTs floated better when air down I found. If you need to kick it into 4WD and you can go almost anywhere.
I would not tackle the first hill as you enter on the left, Sort of a show off hill. It's pretty narrow with trees on either side and a big vertical climb. If you're going with riders on smaller ATVs like a 90 then I'd say you'll need paddle tires.
Is Winchester your only stop?
Two Wire Fox Terriers; Sarge & Sully
2007 Winnebago Sightseer 35J
2020 Jeep Gladiator Rubicon