Horse

A horse was a large mammal native to the planet Earth 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
When visiting the Roman Empire in 120 AD, for example, the Tenth Doctor once sought horses for transport because he deemed them "better" — which was to say faster — than donkeys. (NSA: The Stone Rose) 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)

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) and stagecoaches. (DW: The Unquiet Dead, NSA: The Many Hands)

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.

His fourth self, for example, had no difficulty jumping on to the backs of unsaddled horses in San Martino and galloping away from the threat of execution. (DW: The Masque of Mandragora) He would later ride to Olympus in a flying-horse-draw chariot. (DWM: The Life Bringer)

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

In his eighth life, the Doctor and Izzy Sinclair spent some time in feudal Japan, where they both travelled by horse, seemingly without issue. (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 from keeping it. He later skilfully rode Arthur through a time window disguised as a high mirror, successfully 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 the Confederate West. (NSA: The Runaway Train) Amy Pond was also particularly adept at riding horses and was able to keep up with him on both of these occasions and even rose 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". At the First Doctor's behest, the Greek army constructed 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 successfully behind Trojan lines. This move essentially ended the Trojan War in favour of the Greeks. (DW: The Myth Makers)

Some natural phenomenon, like the Horsehead Nebula and the Horseshoe Crab, 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 then quickly surmised that 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)