Cloudcroft is just under 9,000', somewhat steep grades going down to Alamogordo for sure; with curves & twists. One also goes thru the only hwy. tunnel in NM, not very long good headroom. Some climbing to get from Artesia, but none very severe; lot of curves in areas.
One can also by pass Las Cruces once in El Paso, Take TX 375 Loop (north) off US 62/180; then take US 54 N to Alamo off the 375.
The US 70 route via Roswell & Ruidoso has curves & some grades, but not as great & the Hwy has more multi-lanes (wider). Doesn't get into as high of elevations as well.
If you are planning on doing this trip in the winter or early spring, keep an eye on weather reports. If a snow event has happened or is about to happen, I advise skipping the mountain drives & going US 62/180. But on a re-read of your post I see you're in Cold Wisconsin. Mountain routes would be great in warmer weather, nice break from Carlsbad, etc.
If a wind event is in process or is about to start, Guadalupe Pass is a pass on the US 62/180 route which can be extremely dangerous. Extreme winds in that area at times.
Maybe you can find other info in the earlier post on the
Cloudcroft & Ruidoso & Alamo Areas.
Guadalupe Mountains National Park ---- Guadalupe Pass - Elevation: 5,424'
Near Carlsbad Area - TX/New Mexico BorderIf going to Las Cruces from El Paso area, one must get across a mountain there as well. Trans Mountain Road will take one over the mountain (also TX 376).
One can use the War Road Route to bypass the Trans Mountain pass. These are in Reverse order however: Use Exit 162 in New Mexico (just short of the NM/TX state line) NM-404/Ohara Rd East, turn right on NM 213 S (War Road), this turns into Martin Luther Kings Jr. Blvd (FM 3255) once entering TX. Take the ramp onto Gateway S Blvd/Patriot Fwy (US 54 S) to TX 376 Turn left onto Woodrow Bean Trans Mountain Rd (Texas Loop 375). Follow Loop 375 to the US-62/US-180/Montana Ave exit (about 12 miles). The US-62/US-180 takes you to Carlsbad Caverns. Not mountains to cross on this bypass. If you take a right on 376, then it'll take you up & over the pass.
If you want to take the Pass, just stay on I-10 on into TX. Take the exit toward Texas Loop 375/Trans Mountain Rd (about 5 or 6 miles from state line)....Turn left onto TX-375 Loop W/Woodrow Bean Trans Mountain Rd it will take you up & over (great vistas up at the top, at a rest/viewing area).
Video Drive Trans MountainYou really do not want to drive into El Paso & do a few city streets to get to & onto very busy Montana Ave (US-180 E/US-62 E). Much worse than a mountain pass.
In Las Cruces: Hacienda RV Resort and Siesta RV Park are the easiest to get to, just of I-10 exit 140. Las Cruces KOA and Sunny Acres RV Park off I-10 exit 135. KOA on the mesa overlooking the Mesilla Valley, Sunny Acres in the Valley & a little crowded.
Park Reviews Siesta RV has gravel roads & pads, Hacienda RV has paved roads, maybe concrete pads. Sunny Acres more into town, maybe cramped???
Leasburg Dam State Park is about 17 miles N of Las Cruces on I-25. With
Fort Selden State Mon't near by. A young Douglas Mac Arthur called the fort home while his father was post commander in the late 1880s.
A link to on older post:
Safe RV Parks in El Paso Area. El Paso is a pretty safe place, No Mexican Drug Cartels Shooting up the place. But have no experience camping there.
Just in case your in Las Cruces. Here's some info on the
Las Cruces Area & Southern NM Mexican Food plus camping and attractions in the area. At least try a Green Chile Cheese Burger.
VideoTaste of NM Pecans:
Stahmanns or
Salopek 
