** Click on Title to see full answer ** Interestingly, the military itself has looked at this issue at least a little. In DTIC (Defense Technical Information Center), the search: "carbon footprint" gets 27 reports, on such issues as energy efficiency, public concerns about the military's use of energy, military and other government use of already existing commercial transportation, etc. Even the specific search: "carbon footprint" and iraq gets 4 hits. These appear to be mainly from the full text of fairly popular service members' magazines and newsletters. DTIC is free to all, and even though many reports are NOT full text, it would be worth skimming through other searches such as "energy efficiency" and calculation and iraq (101 hits) to see if there are more technical and detailed reports.
The Department of Energy's OSTI site is a quicker path to full text technical studies, but may not have much on the Iraq war. To shortcut to full text, Look in the Left side column under "Key Resources" and point the mouse to "Science Accelerator" but DON'T click it - go to the menu that opens and click "Information Bridge" which is ONLY full text reports. Or go to the right side of the page and click the "Key Databases" link to find Information Bridge.