hack, hackney
Wikipedia
Beginning in the 17th century, they were originally horse-drawn carriages, later modernized as hansom cabs (1834), that operated as vehicles for hire.
Merriam-Webster
A coach kept for hire; especially : a four-wheeled carriage drawn by two horses and having seats for six persons.
A hack can also be used to describe a horse:
Merriam-Webster
A horse let out for common hire (2) : a horse used in all kinds of work b : a horse worn out in service : JADE c : a light easy saddle horse; especially : a three-gaited saddle horse d : a ride on a horse
