I finally made it up to Elephant Butte for a hike on Sunday, using the route map on the right side of this page.
I'm still recovering from a cold but kept the cough under control by pursing my lips to limit breathing, a tip I got from the doc. I've used the same technique when I've run out of water on long runs and felt constricted breathing coming on. It works. In spite of a pretty vigorous hike I had little coughing during or after.