The 20 billion a year air conditioning cost is marketing nonsense. Specifically, this number comes from someone selling energy-efficient tents to the Pentagon, and it's pretty clear they made up this number. At the very bottom of the article, the Pentagon states it spends $15 billion on energy for all military operations around the world (i.e. everything, not just air conditioning).
Not taken that way. I expect the real number is somewhere between the 20 billion from this article, and the 1.5 billion the Pentagon responded with in their reply. 1.5 billion is probably the line item in the budget that says "tent AC", while different calculations assuming sundry costs can reach higher, and some of it probably is PR inflation.
The main point not being the specific final total, but rather that the cost, and other logistical costs like it, would be reduced or possibly eliminated if troops weren't in the field.
This might be a good time to read Paul Graham's article on PR: http://www.paulgraham.com/submarine.html
(I don't mean this as an attack on araes or the suggestion to reduce military spending.)