A haha has the main intent of keeping the animals of a landscaped park (sheep, cattle, deer) from encroaching on the gardens around the house, yet keep the appearance of a continuous lawn stretching from the house into the far distance. So there's a ditch rather than a raised feature like a fence, and the far slope of the ditch (away from the house) is gentle and grassed. The near side is always a vertical wall, high enough that the animals won't try to jump it. You'll get the dimensions by looking at the real ones around grand houses in England (which mostly have deer parks), that have been found to work. Google 'haha ditch' and click 'images'.
Here, for example:
Might work for deer if you had a straight vertical wall 7 ft tall. Cheaper method might be an electric fence, depending on what you are trying to keep the deer from.
posted 2 years ago
This photo shows a deer ha-ha as it's being used NOW for a deer park. Maybe it's the slopes, but the deer won't cross. In other places, yes - the fences are 8 feet tall, or the deer will cross - especially rutting stags! They're fallow deer, by the way.