In general the hiking around Houston sucks. There is the Lone Star Trail, north of town, through the Sam Houston Forest. Its flat, humid, dense with mosquitos, but the view is great if all you want to look at is the bottoms of pine trees. The closest decent hiking IMHO is Enchanted Rock, west of Austin near Fredricksburg. After that, Big Bend in far west Texas.
Big Bend is a real long haul but there's no place on earth more distinctive than its Chisos Mountains stuck in the Chihuahan Desert and skirted by the Rio Grande. Arm up if you go there, nowadays 2-legged coyotes and drug smugglers make heavy use of the isolated river crossings. The place is a paradise for horseback camping, but it takes an adapted horse to handle the terrain..the little mustangs that live there will do fine, but the country is hard on horses and a flatland horse hauled there won't make it. In the past it was easy to rent good horses in Lajitas but now the fuckin' lawyers have made it very difficult...sure, you can still rent horses...if you don't mind being forced to wear a helmet and being regimented like you was in first grade. Fucking lawyers!