Guadalupe Mountains National Park
This small national park is about 100 miles east of El Paso in west Texas and has the attraction that it is not altogether too cold for a backpacking trip in the winter. My visit was in January. I did a one-night backpack, which is about as long as you want to go because there is no water and you must carry it. I also did a dayhike in an area with many fossils embedded in the rock.