Canyons are inherently risky. Flash floods occur without notice on sunny days. Technical skills & surrounding topography knowledge required yet does not eliminate risk.
This short canyon hike is at the lower end of being considered a canyoneering experience. There is some very minor scrambling up and over small dry falls. There may be more bushwhacking... and crawling around and under large shrubs. The redeeming aspect of the hike is a rocky gorge section that you get to pass through on your way up. Before you climb out on to West Side road you can linger among the tree bound, sculptured rock section. It makes the hike.
To get to this canyon you have to approach up or down Dry Canyon Trail (t5574). You will need to orient from a map or GPS siting. Fortunately, it originates at the only hair pin turn along Dry Canyon trail... from the canyon mouth the trail bends back around and climbs up and away from the drainage; you cannot miss it.
Once on top, you can follow West Side road around to either of the Dry Canyon trailheads... or, head over for one of the other canyoneering routes to follow down and around. If you are hiking from Alamogordo, I'd suggest enjoying Caballero Canyon North as a pleasant return route.
The obvious approach for this canyon from the city is to loop over the mountain using the Ortega/Dry Canyon Traverse. The closest access is the Dry Canyon trailhead off of Hiway 82.
There is a looping option off of the Upper Dry Canyon Trail (t5573) wherein you begin to follow the trail down to the old mine sites, but instead of heading back south along the trail, drop off to the north, re-entering the Arcente Canyon drainage, following any of the downhill routes back into the canyon proper.
This is an easier canyon trek... great for a lazier Fall day.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.