Coat

A coat was a form of clothing worn on the upper body, much like a jacket, but was more substantial in length.

Worn by the Doctor
The Doctor wore numerous coats throughout their life. The First Doctor wore a black Edwardian morning coat, (TV: An Unearthly Child, The Daleks, The Tenth Planet, The Five Doctors, Twice Upon A Time, etc)) while the Second Doctor wore a brown fur coat over his usual attire when visiting locations with inhospitable climes. (TV: The Abominable Snowmen, The Ice Warriors, The Five Doctors)

The Fourth Doctor wore a variety of coats, among them a burgundy velvet frock coat, (TV: Pyramids of Mars, The Masque of Mandragora - The Deadly Assassin) a grey tweed frock coat (TV: The Android Invasion et al) a brown velvet frock coat, (TV: The Face of Evil et al) a light brown Harris tweed frock coat (TV: The Power of Kroll et al) and a plum velvet trenchcoat with green lining. (TV: The Leisure Hive onwards) He also briefly adopted a overcoat as part of the chauffeur uniform he used in an attempt to gain access to Harrison Chase's mansion. (TV: The Seeds of Doom)

The Fifth Doctor wore two similar frock coats, one with a lighter beige hue (TV: Castrovalva onwards) and another that was dark grey. (TV: The Awakening onwards) The Sixth Doctor initially wore a patchwork frock coat with several different colours and fabrics, (TV: The Twin Dilemma onwards) which he replaced with a similar coat in different shades of blue for a period (AUDIO: Real Time onwards) before returning to the original. (TV: Time and the Rani) The Seventh Doctor wore a duffel coat over his usual attire during his visit to Maiden's Point. (TV: The Curse of Fenric) and also a black leather trenchcoat on Nazi Germany. (PROSE: Timewyrm: Exodus)

The Eighth Doctor wore a green velvet frock coat for much of his early life, (TV: Doctor Who, AUDIO: Storm Warning, Blood of the Daleks) replacing it with a similar one in blue after his original was destroyed onboard the Ophidius (COMIC: Ophidius) up until its demise on Earth in 2005. (COMIC: The Flood) For a time, he wore a navy blue leather peacoat. (AUDIO: The Great War) Later in his life, he had adopted a bottle green moleskin overcoat. (COMIC: The Pictures of Josephine Day, TV: The Night of the Doctor)

The War Doctor wore many leather trench coats on black (COMIC: The Whole Thing's Bananas) or brown (TV: The Name of the Doctor, The Day of the Doctor) The Ninth Doctor also wore a black leather peacoat. (TV: Rose, onwards)

The Tenth Doctor often wore a cinnamon brown overcoat over his regular attire, (TV: The Christmas Invasion onwards) while the Eleventh Doctor wore both a olive green moleskin overcoat (TV: Let's Kill Hitler et al) and an eggplant cashmere frock coat (TV: The Bells of Saint John) on various occasions. He also adopted a Victorian frock coat on two occasions, (TV: The Snowmen, The Time of the Doctor) and used a military greatcoat as part of a ploy to confuse Kahler-Tek during his visit to the town of Mercy, Nevada. (TV: A Town Called Mercy)

The Twelfth Doctor's outfit initially featured a navy blue crombie coat with cimson lining. (TV: Deep Breath) During his travels with Clara Oswald, he adopted a new burgundy velvet coat. (COMIC: The Highgate Horror, TV: Face the Raven) He also wore a black velvet frock coat. (TV: The Pilot, Thin Ice),

The Thirteenth Doctor took to wearing a hooded, lilac-blue trench coat with a dark blue interim and a rainbow pattern across the edges of it. (TV: The Woman Who Fell to Earth) While in 1955 Montgomery, Alabama, she intentionally tore her coat. She and Yasmin Khan gave the coat to seamstress Rosa Parks to repair to ensure she would leave work on time on the day of her historic arrest. (TV: Rosa)

The Fugitive Doctor wore a navy tweed frock coat. (TV: Fugitive of the Judoon, The Timeless Children, Once, Upon Time)

The Curator resembling an older Sixth Doctor, wore a violet moleskin frock coat with a silver cat brooch. (AUDIO: Crossed Lines)

The Doctor who posed as Merlin wore an afghan coat (PROSE: Transit).

Worn by companions
Captain Jack Harkness often wore a large blue RAF issue greatcoat. (TV: The Doctor Dances onwards)

Amy Pond wore a dark teal trench coat during her encounter with Vincent Van Gough. (TV: Vincent and the Doctor)

Josie Day wore a double breast tail coat done on steel blue without sleeves. (COMIC: A Matter of Life and Death, The Lost Dimension)

Romana wore a scarlet frock coat. (TV: The Horns of Nimon)

Sarah Jane occasionally wore trench coats. (TV: Eye of the Gorgon, The Last Sontaran, Mark of the Beserker, etc)

Donna Noble wore a winter coat with a furry hood on the Ood Sphere. (TV: Planet of the Ood) She also wore a caramel brown leather trench coat. (TV: Blink, The Stolen Earth|Journey's End)

Bill Potts wore an emerald green velvet coat during a visit to the 1814 frost fair. (TV: Thin Ice)

Worn by the Master
The Master occasionally wore coats.

The incarnation who possessed Bruce wore a duster coat of black leather. (TV: Doctor Who)

The bald incarnation wore a black overcoat when posing as 'the other Doctor'. (AUDIO: Dominion)

The war incarnation wore a maroon moleskin coat when he met UNIT and the Cybermen. (AUDIO: Master of Worlds)

The 'Saxon incarnation' wore a black frock coat when he met the Twelfth Doctor. (TV: Time and Enough|The Doctor Falls).

The 'Spy incarnation' wore a frock coat of plum purple tweed when he met the Thirteenth Doctor. (TV: Spyfall, Ascencion of the Cybermen|The Timeless Children)

Worn by others
While impersonating racing pilot Horation Hamilton, Zalenby wore a long leather flying coat and silk scarf. (PROSE: The Game of Death)

Jackie Tyler intended to slip a tenner in Elton Pope's coat pocket to pay for the pizza he was getting. However, Jackie found a photograph of her daughter in his pocket. Realising that Elton was using her to find the Tenth Doctor, Jackie angrily sent him away. (TV: Love & Monsters)

Sally Sparrow wore a brown trench coat. (TV: Blink)

Jackson Lake wore a mustard brown tweed overcoat with a burgundy overcheck. (TV: The Next Doctor)

The Second Rani wore a black trenchcoat when posing as Professor Baxton. (AUDIO: The Rani Elite, Planet of The Rani)

Shortly before her death at the hands of the Toclafane, Vivien Rook gave her coat to Tish Jones as she spoke with Lucy Saxon. (TV: The Sound of Drums)

Sutcliffe wore a royal blue tail coat. (TV: Thin Ice)

Webley wore a double breasted frock coat of bottle green tweed with a scarlet overcheck. (TV: Nightmare in Silver)

Frank wore a raincoat and brogues, which he got muddy. (PROSE: The Party in Room Four)