From Nogal, take highway 37 and forest road 107 into the White Mountain Wilderness. The hike to Argentina Peak is found among the campsites at the end of the road.
Note that GPS coordinates are approximate, derived from Google Maps (my camera does not record them).
Hiking along the Crest Trail in the White Mountain Wilderness, we encountered dozens of paintbrush and irises in bloom. These hugged the downward slope toward the Tularosa Valley, thousands of feet below.