To suggest that a large majority of the current refugees are not post-war is nuts -- there's no lack of documentation of the huge flows into Syria, Jordan, and other neighboring countries in the last few years.

Looking over older UNHCR documents and 2003 vintage news reports, the estimates of Iraqi refugees at the time seem to have been several hundred thousand -- maybe 20% or less of the current total of more than 2.6 million (their "over two million" in the text is rounded down -- add up the numbers in the tables). And, note that for most countries those were figures from January 2006 -- 18 months ago! Since reports are quite consistent that heavy flows out of the country continue (according to Jordanian military officers I've spoken with recently as well as news reports -- they're quite concerned about how their country is absolutely bursting with post-2003 refugees), that's got to be well above 2.6 million now. Plus, there were tens of thousands, maybe even more than 100,000 returns in the early post-Saddam period, so the total fraction of the 2.6 million plus who are recent refugees is likely even higher. Bottom line: it's doubtful that more than 10%-15% fo the current total are pre-2003.

One clue might be that the total number of internally displaced persons increased by 50% just from February 2006 to April 2007.