As of July 3, 2010 -- the only information that I have for NAS Fallon's Stables...

The May Ranch Stable offers active-duty military personnel

a place to board their horses while stationed at NAS Fallon.

This facility, located on the south side of the base,

has accomodations for 20 horses with many extras,

including an indoor arena, two round corrals, and a large outdoor arena. 

I believe MWR operates the facility -- but am not sure.

If anyone has any additional information -- I will happily post it!!

Also -- in the area --

the Churchill County Fairgrounds will board horses overnight.