Canyons are inherently risky. Flash floods occur without notice on sunny days. Technical skills & surrounding topography knowledge required yet does not eliminate risk.
Horse Ride without the Gee!
This Ridge forms the north side of Beeman Canyon, and effectively is the last access up into the mountains from Alamogordo, taking off from the north end of town. Route finding is simple if hiking down the ridge. You have the option of walking up on the crest, looking west into and across the Tularosa Basin, south on down the frontal range, east and north over into Dry Canyon, seeing Sierra Blanca in the far distance. Or, you can drop down slightly into Beeman Canyon and walk the top of the cliff edges. That offers the better views and some very nice walking.
If you are hiking from the bottom, you have to choose which feeder ridge to hike up. It does not really matter, but there has been a pattern of use on the ridge that begins a bit further up and into Beeman Canyon. If you choose not to head up the obvious longer ridge on your left, then hike up the wash or old jeep track (they both end up the same place) and once in site of the secondary ridge, make your move to the left. If you're lucky (?) you might spot some old cairns or ribbons posted by some horse riders. For some very odd reason they marked this ridge route for quite aways up... even once on the ridge.
Once on the ridge it is simple... keep moving up! It looks steep, but really is a fairly easy hike for off trail ridge hiking. You will eventually top out at the little peak point above the narrowing of Beeman Canyon. From this point on, consider angling down towards the cliff face below you on the right, then simply follow the cliff edge around Beeman Canyon. It will offer great views of the Jumble, the congested rock maze in the bottom of Beeman... then later, just pleasant walking as you wind your way around and up into and above the North Fork of Beeman Canyon. Once above and past the Forks, the ridge continues up following the North Spur, the furthest north drainage of Beeman Canyon. Looking down you'll note the old jeep/ATV tracks riding the ridge between the Spur drainage and the North Fork drainage... leading up to the meadow and connecting with the Forest Service 4 wheel drive route up to the top of Horse Ridge and Winter Peak.
If you are hiking up the ridge, you may want to consider looping back down the North Spur... and enjoying the pleasant hiking and down climbing through the Jumble in Beeman Canyon. If you continue on up past the meadow, you will be walking the jeep road. Probably will not be too many vehicles, but they are possible. The noise you hear is the boom of guns... the most popular target practice range is off Hiway 82 in Dry Canyon, below you to the North.
The real way to enjoy Horse Ridge is to down hike it, using it as the second half of a loop after coming up Beeman Ridge, Beeman Canyon (any of the 3 routes)or any route that takes in Winter Peak.
Mileage and elevation for your hike will be determined by just how far up you go.
The plants and rocks along the ridge are all sharp and prickly. Nice to have gloves along. As with all off trail environments, most of the rocks are not stable. Walk carefully out there!
You can drive closer into the mouth of Beeman Canyon, but I prefer to leave my car out along the Scenic Drive Blvd, parking in the church parking lot or at the Maze. Use your own judgement...the gravel track off of Scenic (behind the church) is rough... and the chances for vandalism have to be greater back in there.
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.