A long-time collector of live oaks in Texas (and those aren't the same species as this, so FWIW) told me that he chopped the top and most of the branches off of what he dug at collection ,got as much root as possible. Whatever foliage remained on the tree was left. From what he said, the trees that survived the collection process dropped all the existing leaves and pushed a new crop, while the trees that didn't survive held onto their leaves and browned out never to return.
This was with Escarpment live oak (quercus virginiana "fusiformis," which is also called quercus fusiformis). I have no idea if it applies to this desert species, though.
Also FWIW, NEVER chop a tree to its "final" height in the field. Leave some extra length on the trunk to work with. Wait for new growth, choose a new bud that hopefully forms at the right place on that length as the new leader, then chop it. That process can take a year or more. Rushing to cut a newly collected tree into a final design never ends well...
And yeah, it snows in Arizona. The state has some fantastic ski resorts, just like New Mexico.
http://www.skithelemmon.com/
http://www.arizonasnowbowl.com/?q=webcams