Ozz, take I-27 South from Amarillo, to US 60 West at Canyon. Stay on 60 to Clovis, NM, then take US 70 South to Portales, Roswell, Ruidoso, and Alamogordo, to Las Cruces. You will cross 2 mountain ranges, the Sacramento and the Organ Mtns. Both are passable year round unless there is a freak storm. The roads were good to excellent the last time I went across there. Lots of big trucks take this route, so they keep it in pretty good shape.
Another way would be on US 60 through Clovis, Ft.Sumner, Vaughn, and Mountainair, to I-25 at Bernardo, then south to Cruces. This route is the easiest as far as mountains go, and the roads are good, but only 2 lane, and the weather is sometimes unpredictable around Vaughn and Mountainair.
Honestly, I wouldn't be afraid of either route.
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