Iraqis Celebrate Christmas?

It's December 25th in Iraq and the Christian population celebrated the birth of Christ in a private setting.
Muslims regard Jesus Christ as on of the most important prophet sent from God. However, in Iraq this year Christmas day coincided with the start of Ashoura--one of the most important dates in the Shiite Calendar, it marks the death of Imam Hussein, one of the founding martyrs of Shiite Islam.
Christian all over Iraq refrained from the Christmas celebration out or respects of their Muslim neighbors, but also out of fear?

This year only one church held midnight mass in Baghdad and Christians voluntarily keeping Christmas behind doors. It is very strange since no Islamic leader or official asked them to do so. So it is quite confusing whether or not it is out of pure respect for the majority religious group or out of fear.
In 2003 Christians started leaving Baghdad, there were about 1200 Christians living in Baghdad then, today there are fewer than 500. Most of the Christians sold their assets and emigrated, since there were splits within the ethnic groups and armed factions had risen.
Christians have been targets of Islamic militant groups.