'Private Road' means just that. Signs on either side of the road stating 'No Trespassing' means stay on the road, provided you didn't miss a "Private Road" sign. If you come up to a gate with no signs, you are okay to go through it. Just leave the gate in the state that it was in when you came upon it. The gates are usually there to control open grazing. Leave open if it's open or close it behind you if it was closed. This is very common and most hiking, 4X or climbing type guides will tell you that.