As you can see here, Obama's reception was enthusiastic. Of course there's no point in going to Baghdad and getting cheered at by troops if no one else can see it, so the White House pool came along for the ride—which was, naturally, a very hush-hush affair.
In fact, as TV Newser reports, Obama left all the White House correspondents who had been following him on the European trip behind in Turkey. They all thought he was headed home, which is why Chuck Todd posted this to MSNBC's First Read this morning about 30 minutes before Obama touched down in Baghdad:
The only network correspondent who was on Air Force One for the trip was CBS News's Chip Reid, who was acting as the pool reporter. Ironically, the only major network that didn't break in with a special report when Obama landed was CBS.
And for comparison purposes, here's video of Bush's final visit in December of last year to the land he destroyed, as he greets his very white, very country-music loving army.