What are the origins of the phrase "field day" as used to refer to cleaning of a military barracks?

Solution 1:

According to phrases.org.uk, field day has a meaning of

A day of excitement or a circumstance of opportunity

with the first reference being in 1747, in A Scheme For Equipping And Maintaining Sixteen Men Of War: Of Twenty Guns Each

...as it were Field Days, for improving and approving their Valour and Prowels...

As you mentioned, this is often used with the idiom "Have a field day". Two things stand out to me here:

1) A field day, in a militaristic sense, refers to the opportunity to both prove and improve ones ability to accomplish required tasks. This could refer to battlefield maneuvers, but it could also refer to more simplistic tasks (such as cleaning the barracks).

2) As a field day originally referred to a chance at practicing, the difficulty involved should be minimal. This would draw a clear connection with, for example, reporters being handed a story that is easy to write about. In my opinion, it is considered a field day because the task at hand is uncomplicated and straightforward, requiring a minimal amount of skill in order to succeed.

In combining those two points, field day as it refers to the cleaning of the barracks, is a chance for a unit to show that it is able to accomplish simple tasks efficiently.

Solution 2:

A Field Day is a result of the ROE for a training schedule. Each military organization MUST post a training schedule for the month which is adjusted weekly. The days needed to train not in Garrison but in the field were pre-scheduled as a simple place on the training schedule for the month for scheduling purposes. The week prior would be adjusted identifying the actual event (23/07/2016 Firing Range),thus giving the Soldiers the time needed to prepare the equipment needed in advance.