For Chicken Corners, there is an adventure camp a ways past Hurrah Pass that a loaded down (supplies in, garbage out) pickup truck travels too just fine. Lots of smaller 4x4 trucks/SUVs on that road. Beyond the camp turnoff there are a few tough places, 4x4 stuff due to the sandy steep nature or a good ledge. Lots of room. Just a curvy steep soft climb.
The word trails was used, so these are for bikes/peds maybe some for ATVs. Tons of suitable roads though. Pucker Pass (Long Canyon) have to watch total height though, you have to pass under a fallen rock. The worst steep part that is narrow and had a bit of ledge was graded a bit recently, easier now. Got to watch the deep sand on some of the stuff to the NW of Hwy 313. My favorites are Spring Canyon Bottom Road, Onion Creek, Potash Road, and Gemini/Long Canyon loop. Many more. None of these are known as trails though.