Use a variety of maps: onX, County Road Maps, Topo Maps etc. Very often ranchers want roads to look private even though they are County. If my sources label a road as County and it's unlocked I feel pretty comfortable in driving it.
If it shows as County but is locked then the only way to be sure would be to call the County and sort it out - probably not happening during a hunt.
There are numerous instances of private landowners figuring out creative ways to take ownership of County roads (legal manners). For instance I know of a road in Roswell area that accessed Barbary Sheep hunting areas. The guy in charge of County road maintenance intentionally didn't maintain it for a year, at which point ownership reverted to the private landowner - one of his relatives, go figure. So now it's a huge maintained County road to a (legally) locked gate. Beyond the gate the road appears identical: it was built by the County and maintained as such for years. But now it's inaccessible to us. Shenanigans like this happen all the time.
Or an underhanded deal will pop up to transfer land or road ownership say around Roswell. It's required to be advertised publicly for comment. And it will be advertised in Raton...
Best of luck!