Wayne:
It seems to me the haha is used more frequently in major applications of landscape architecture and such---eg Ardrossan Farm and other English country estate type applications---not really on a dairy farm. I believe the idea of the haha (trench or wall) is to make the division between a lawn, for instance, and the more distant fields in which cattle graze appear seamless or non-existent (ie "natural"). From a mansion house, for instance, as one looks across a massive length of lawn it appears the distant cattle could wander onto the lawn but of course they can't as they can't cross the haha that one can't see at the far end of the long expanse of lawn. The haha was a landscape application alternative to fencing in certain spots since fencing is visible and breaks up the look of the distant but planned natural appearing view.
A really good ecample of the use of a haha on a golf course (in this case it hides a maintenance road across a fairway) is on the end of the fairway on the 4th hole at Hanse's Applebrook G.C.