Why would they shave the horses?

[Scroll down and you'll find the answer. - Dave]

It was, and is, also known as the Great Alpine Highway, although the name of the road changes from "West Coast Road" to "Otira Highway" when it enters the West Coast Region (Te Tai Poutini). The views can be quite spectacular, especially as it passes through gorges.

sitting on the bench next to the driver -- I believe we have Sherlock Holmes and Dr. Watson on the case of Murder in New Zealand.

would call it high and tight, equine version.

... they didn't just shear sheep on South Island.

That tonsure is called a trace high clip. It allows the horses and mules to keep their natural blanket on top while airing the sweaty bits below.

This rather large type of stagecoach was often referred to as a diligence. They were intended to carry more passengers than the smaller fast moving coaches, with some models reportedly designed for as many as sixteen. The trade off was that they were a bit slower. For older travelers or those not in a hurry, this was sometimes an attractive feature. In an age when roads were rarely paved and often had deep ruts or holes, travel at speed was frequently uncomfortable and sometimes downright dangerous.