You need to take a look at the map for the particular forest. If it's just a logging trail cut into a hillside by a skidder then it's not a road. However, if the road is shown on the map of the forest and it's maintained by the state, then it's considered a public roadway.

26-66-1
(e) No hunting weapon shall be discharged toward any person, building or domestic animal when the same is within range or from or across the traveled portion of any public roadway.

(i) Hunting is prohibited from the traveled portion of a public road or on any road adjacent to any premises used for the breeding, rearing, or holding in captivity of wildlife, or premises used for zoological purposes, or posted by the Department or its agents against said activity.