Go to the county courthouse assessor's office or get some forest service/blm maps to check the land status of the dirt you're interested in (you should be aware who owns it). As Dog said, stay off the off-limits res land unless you have permission - keep in mind that a great deal of res land is open to the public. Other than 'private' Indian land, you can go anywhere you want as long as the fence and/or gate isn't posted. If it is posted, be careful and don't leave footprints (you'll be walking). If you do get caught, admit to your ignorance and ask for forgiveness. Tell 'em you're looking for your dog. As Clay mentioned, you're better off avoiding all terrain too close to the Mexican border, including, sadly, gummint land.