They're not just to protect from animals. You'll often find them in gardens where the area below isn't even open to livestock. The other reason for these is to hide unsightly parts of the view. If there is a road, village or other buildings in front of the house, for example, building a ha-ha could make it look like the park stretches unbroken to the horizon. It could also make it look like distant hillsides are part of your park if your own land is a little on the small side.

Source: my wife is a landscape archaeologist, specialising in post-medieval parks. We visit a lot of stately homes.