I'd be willing to bet most of the land around the Davis Mountains is privately owned. There is a big loop around the Davis Mountains, and if you want some dirt trails and a hint of risk (mainly because nobody drives the road so if you break down you may be walking) take Pinto Canyon Road out of Marfa and it hits 170 along the border. Its a cool road, very scenic. But you won't see too many people. Last time I went down it we came across a guy in a Jeep. He had stopped to take photos and when he got back in the thing would not start. He had been sitting there several hours and we were the first vehicle to drive by.