Hey Craig, my vote is for the Gila Wilderness. 2 hour drive from El Paso, TX to Silver City, NM via I-10 and you can be in the backcountry about 30 min. after heading out of Silver City, NM into the Gila National Forest. You can head out into the wilderness from the Gila Visitor Center and either hike west up the West Fork of the Gila River or travel up the Middle Fork, both routes offer plenty of water and great views of the canyon above you and numerous intersecting trails to make loop hikes out of your 2-3 days. Temps can be pretty frigid at night though, teens and 20's are typical for Feb. and snowfall is always a possibility, although precipitation is very minimal (appx. 0.66" for month of Feb.), most of the major weather fronts hit the higher elevations to the west in the Mogollon Range (9,000-10,000+ft.) which are usually sacked in with snow until May or June. Daytime temps in Feb. avg low to mid 50's, although Feb. is a spotty month and you can get a high of 65F one day and a high of 25F the next. Crowds during that time of the year are non-existent. There are a couple hot spring diversions in the Gila Wilderness which are nice destinations especially in late winter.
Since water is a condition of yours Guadalupe National Park is out of the question I assume, although beautiful and only 1 hour drive from El Paso International Airport. If you're willing to tote water then this is a possibility.
Maybe someone else can chime in on Northern NM, but I know most places up there will be quite cold and snow will be an issue.