Horse

A horse was a large mammal native to the planet Earth. It was used for transportation, sport and companionship. So intertwined were horses with humans, that horses were the bases for many cultural references.

As transportation
Humans used horses as transportation for thousands of years. They could be directly mounted or used to pull vehicles.

As mounts
In 323 BC, Alexander the Great taught the First Doctor's companion Ian Chesterton how to ride a horse. (CC: The Time Museum)

When visiting the Roman Empire in 120 AD, the Tenth Doctor once sought horses for transport because he deemed them "better" — which was to say faster — than donkeys. (NSA: The Stone Roses) Around the same time, the Eleventh Doctor, Amy Pond and River Song used Roman horses to cover the distance to Stonehenge. (DW: The Pandorica Opens)

In 1006, King Sitric Silkbeard of Dublin rode his horse Sleipnir, to whom he often spoke if he were a person, on a three day journey from Dublin to the Abbey of Kells to retrieve the Book of Kells. (BFA: The Book of Kells)

Geoffrey de Lacy rode his horse from London to find John of England's castle. The journey took him only four hours. Horses were also used in a javelin match in the 13th century to settle arguments. They were very popular modes of transport. (DW:  The King's Demons)

As beasts of burden
Horses could be used to pull vehicles, such as chariots (DW: The War Games), carriages (DW: The Unquiet Dead; DWA: Highway Robbery, BFA: The Doomwood Curse, DW:  The Visitation) stagecoaches (NSA: The Many Hands) and hansom cabs (DW: The Evil of the Daleks, DW: The Talons of Weng-Chiang).

In sport
Horses were also used — at least in England — as mounts in jousting tournaments. (DW: The King's Demons)

Horses and the Doctor
The Doctor was an adept horseman in many incarnations.

The Fourth Doctor had no difficulty jumping on to the backs of unsaddled horses in San Martino in 1492 and galloping away from the threat of execution. (DW: The Masque of Mandragora) He would later ride to Olympus in a flying-horse-drawn chariot. (DWM: The Life Bringer)

The Sixth Doctor once rode on a horse in an attempt to catch up with Astrolabus. (DWM: Once Upon a Time Lord)

In his eighth incarnation, the Doctor and Izzy Sinclair spent some time in feudal Japan, where they both travelled by horse. (DWM: The Road to Hell) Later, the Doctor spent time riding with the Lakota Sioux. (DWM: Bad Blood) While on board the SS Madame de Pompadour in the 51st century, the Tenth Doctor came across a horse he called Arthur, which had presumably crossed over through a time window from the 18th century. It followed him around the ship for a while, but Rose forbade him to keep it. He later skilfully rode Arthur through a time window disguised as a high mirror, breaking the system the Clockwork Droids had built. Arthur was thus instrumental to freeing Madame de Pompadour from the Droids. (DW: The Girl in the Fireplace)

Later in his life, the Doctor's eleventh incarnation showed considerable prowess with horses not only at Stonehenge in the 2nd century AD, (DW: The Pandorica Opens) but also on the American frontier. (DW: A Town Called Mercy, NSA: The Runaway Train) Amy Pond was also particularly adept at riding horses and was able to keep up with the Doctor when they rode together. She even rode a horse on Olympus amongst the gods. (DWM: The Chains of Olympus)

Cultural references to horses
One of the longest-standing cultural references to horses on Earth was that of the "Trojan horse". Aware of this reference from history, the First Doctor then in turn suggested the idea to the Greek army that they build a giant wooden statue of a horse and presented it to Troy. Unbeknownst to the Trojans, the Greeks had secreted themselves inside the moveable statue and sprang a decisive attack upon the Trojans once they were behind Trojan walls. This move essentially ended the Trojan War in favour of the Greeks. (DW: The Myth Makers)

Some natural phenomena, like the Horsehead Nebula, were so named by humans because of their similarity to the anatomy of horses.

Horses were a common adornment of fairground carousels. Once, the Eighth Doctor thought that the TARDIS' chameleon circuit had accidentally started working in Nazi Germany, turning the police box into a carousel. Testing the new shape, Lucy alighted one of the fake horses and engaged the wheel. The Doctor quickly concluded the TARDIS had not in fact changed into a carousel. (BFA: The Scapegoat)

In the English language, "horse" sounded similar to the word "host". This resulted in the Jixen warrior, Jixey, referring to himself as a horse when he made a mistake after just having learnt English. He intended to inform Starkey that he was his host. (K9TV: Hound of the Korven)