Was Iraq colonized?

Officially, No, but many consider it to be because the power that the British exercised over Iraq during its mandate-period resembles colonization.

Iraq was part of the Mandate System and as such, the British expended a great deal of manpower to "modernize" and "control" the country. Officially, however, mandates were not colonies in that a mandate has the future purpose of becoming a realized independent state. A colony does not have such a purpose. The Mandate of Iraq was maintained from 1919 until 1921 when the British transferred authority to King Faisal I. However, the British interfered often with Iraqi policy and maintained boots on the ground until 1954.