Where do you plan to stay in Sow Low? The reason I ask is, due to the high elevation, this is a summer destination and most RV Parks are closed during the winter months. However, It is also ski area, since Show Low is in very close proximity of the White Mountains.
As far as your driving route is concerned -- At Las Cruces get on I-25 and go north to Socorro, from there get onto R 60, going west and that will take you right into Show Low. This will give you good, easy driving.
Mariekie from Tucson AZ