Horse buggies are a very traditional mode of transport on Spetses. They are not something you will find on many other Greek islands.
They are usually favoured for short trips, e.g going on a sightseeing trip of the old harbour (Palio Limani) from the Dapia harbour or getting to some of the nearer beaches. They will also transport you to and from your accommodation, but will have a limit on the number of passengers and the weight of the luggage.
They can be pre-booked or potential passengers can just hail one and jump in.
They are very popular for weddings and will decorate the buggy with fresh flowers.
There is a price list in the Dapia where they have their 'horse stop' and like the bus, they also have another 'horse stop' on the Poseidonion jetty, to service the west side of the island.
Check prices before you jump in.