They're neither comfortable nor cheap, but make for an easy way to get around the island.
The trip should take around 30-45 minutes to go the whole way around non-stop, but it is more enjoyable if you break it into a few hops. We used the lovely Nan, who appeared to treat his horses well (they never work mornings and only one horse is used per day). You can reach him on T: 0818 0379 4040.
Starting price for a ride around the island is 150,000 rupiah. Bargaining is recommended, or at least settling on a price before you head off.