Tibetan Yeti

Tibetan Yeti, also known as Abominable Snowmen, were anthropoid creatures that dwelt in the Tibetan Himalayas on Earth.

Species
By 1984, three species of Yeti were formally identified and classified: "Mih-teh" and "Dzu-teh", which were large apes, and "Yeti Traversii", found by Edward Travers, was more bear-like and very timid. In 1984, the London Zoo had a female Yeti Traversii named Mahamaya, which was successfully bred with a male from Peking. Their child was named Margaret for the Prime Minister Margaret Thatcher, whom she bit at a photocall. (PROSE: Downtime)

History
Little was known about them, except that they were large, furry, probably semi-sapient humanoids. They were timid, rarely approaching travellers, and most in the western world believed them mythical

The First Doctor, Dodo Chaplet and Steven Taylor encountered a pack of Yeti near the Det-Sen Monastery in 1630. Dodo befriended some and recruited them to help protect the monastery from a gang of bandits. (AUDIO: The Secrets of Det-Sen)

Professor Travers went on an expedition to find them in 1935 to prove that they actually existed. After an adventure with the Second Doctor and the Great Intelligence's Robot Yeti, Travers believed he had spotted one and went in pursuit. (TV: The Abominable Snowmen) However, according to most accounts, this Yeti turned out to just be a surviving robot. (PROSE: Times Squared) Capturing it, Travers brought it back to London, where he showed it to the War Department. The report was not taken very seriously at the time, but, by 1963, had been reappraised following the British Rocket Group's unambiguous discovery of extraterrestrial life in 1953 (which was covered up for the general public, but widely circulated in the higher spheres of government); it thus played a part in the creation of a government agency devoted to defending against hostiel extraterrestrial incursions, (PROSE: Background) the Intrusion Counter-Measures Group. (TV: Remembrance of the Daleks) Years later, Travers did not appear to possess any proof of the species' existence. (TV: The Web of Fear)

Decades later, a team of monster hunters attempted to photograph the elusive Yeti and were captured by the Great Intelligence responsible for the creation of the Robot Yeti. Lama Gampo, a monk who had sworn to protect the world from the Intelligence, blew a great horn and called the real Yeti, who howled in response and descended the mountains to fight against their robotic counterparts. (COMIC: Yonder... The Yeti)

In 1984, the Yeti was formally classified. (PROSE: Downtime)

For the Into the Unknown blog, Professor Grey cited the Himalayan 'Yeti' as an example of "the strange and the enigmatic", stating that it, among other mysteries, "fascinate[d] and enthral[led], and the allure of paranormal mysteries remain[ed] strong, even in this (supposedly) enlightened age". (PROSE: About This Site)

Possible sightings
A Yeti was in the Death Zone on Gallifrey when several incarnations of the Doctor were summoned there by Borusa during his quest to claim immortality from Rassilon. (TV: The Five Doctors)

During their journeys in the 20th century Bea Nelson-Stanley and her husband Edgar saw young Yetis frolicking in the snow. Bea thought they were wonderful. (PROSE: Eye of the Gorgon) According to Bea, the Sultan of Ishkanbar had also seen a Yeti. (TV: Eye of the Gorgon)

The Museum of Things That Don't Exist had nine different varieties of Yeti that all supposedly didn't exist. However, the exhibits weren't known for their accuracy. (PROSE: The Taking of Planet 5)

Snowmen "Real" Yeti
The question of whether there are "real" Yetis in the Doctor Who universe is not possible to definitively answer just from televised episodes alone, and the answers present in expanded universe media show a similar lack of unified clarity on the subject.

One may have appeared at the end of The Abominable Snowmen, but the script is considerably unclear as to this point. According to production records of the now-wiped serial, the supposed "real" Yeti would only have been briefly glimpsed in a long shot, and it may have been depicted with a slightly "slimmed-down" version of the robot Yeti costumes. Whether that would have been enough for viewers to actually detect a difference between the "real" and robotic Yeti is unknown. Certainly, production records indicate that a close-up of a "real" Yeti has never been shot for televised Doctor Who.

A possible image of the "real" Yeti of Abominable does exist, taken as a telesnap, which is a photo taken of a TV during the episode's broadcast. The certainty about this image coming from this scene is not absolute, but this is the policy of the BBC.

In The Web of Fear, a robot Yeti is placed in a museum and is said to have been brought to London back by Travers. Some stories tend to suggest that this robot Yeti was the one he was chasing after at the end of his first story, such as 1995's PROSE: Background. The 2016 Lethbridge-Stewart novel Times Squared similarly mirrored that the Yeti spotted by Travers was simply yet another robot.

On the other hand, the Target Books novelisations Doctor Who and the Abominable Snowmen and Doctor Who and the Web of Fear refer to "real" Yetis in ways that the televised episodes don't. The Snowmen novelisation gives a vivid depiction of the difference between living and robotic Yetis. In the Fear novelisation, Travers even mentions the real Yetis, something not in the TV story.

The 2022 animation of Snowmen explicitly illustrates the real Yeti near the end as being entirely different from the robots featured in the story, making it seem almost certain that the Yeti can not be another robot.

Collecting all this together, it generally seems that the intent in the 1960s was that the Yeti is real in-universe, but that expanded media by future authors were much more cynical about the topic.