Exactly where, I don't remember, there is a discussion about the overall sequencing of different tests to minimize refurbishment, etc. It's really dependent on what you or your customer intend to do with the environmental qual. As a general rule temperature and vibration are the big hitters. Most others tend to get by with verification by analysis.
AR 70-38 is actually more of a weather conditions document and has really been superceded with MIL-HDBK-310, although, AR 70-38 does contain some extra material. Moreover, MIL-STD-810 does contain most of the testing-related pertinent information with respect to temperature, solar load, etc.
If your program requires it, you might also need to consult MIL-STD-461, -462, -464, which relate to EMI/EMC testing. Army programs tend to want ADS-37A, which references the other specs in most cases.
TTFN