A press release reported on by EW.com on October 18, 2010 states:
Disney, Paramount Pictures, and Marvel Studios have announced via press release that Iron Man 3 will be released in on May 3, 2013.
This suggests that Iron Man 3 was always intended to be a late spring tent-pole picture in keeping with the previous releases.
We can only speculate the reason behind the Christmas theme, but in my opinion the sense of conclusion to an over all arc spanning three films fits well with a story set at the end of the year; 'out with the old, in with the new' you might say.
Also, I believe that the events in The Avengers occurred in the summer, which would be recent enough for Tony's PTSD to be so crippling.
I was planning to add a whole lot about Shane Black's predeliction for xmas in his stories - but Oliver C. has done the grunt work for me - see his answer above.