Chances are, that any trail or route described is in an area with written rules about hiking with dogs. For the most part the National Forest sites have this information available. National Forest rules are usually vague about leashes in the forest, but very specific about leashes in developed areas. It is typical to read “Pets must be on a handheld leash at all times”, for Wilderness/Recreation areas and developed campgrounds.
When visiting a new area it’s best to check city, county, ranger district and then Forest Service for leash laws.
Respect private property and know where you’re going before you get there. I personally use BackcountryNavigator Pro on my Samsung with the BLM property line overlay. This is still no guarantee that you will be on public lands. If you see signs, err on the side of it being private land.
Practice “leave no trace” when visiting the forests. Or any time you’re out with your dog ideally. In particular, DON’T leave a bagged poo anywhere. Carry it or shove it in a pack.