Trenchcoat
Trenchcoats' were coats made for protection from weather, famously worn on wars.
Worn by the Doctor
The Fourth Doctor wore a single-breasted trenchcoat of plum purple velvet when he and Romana II foil Tryst's conversion of Mandrels into Vraxoin. (TV: Nightmare of Eden) He also wore a burgundy trenchcoat, (TV: The Leisure Hive) up to his death. (TV: Logopolis)
The Seventh Doctor wore a black leather trenchcoat on Nazi Germany. (PROSE: Timewyrm: Exodus)
The War Doctor wore double-breasted leather trenchcoats on black (COMIC: The Whole Thing's Bananas) or brown. (COMIC: The Clockwise War, The Lost Dimension, Four Doctors; TV: The Name of the Doctor, The Day of the Doctor)
In World War I, the Ninth Doctor wore a British Army trenchcoat. (COMIC: The Forgotten)
The Thirteenth Doctor wore a hooded, periwinkle trenchcoat with midnight blue interim, apart from the sleeves, which had lavender insides, and a rainbow pattern along the edges. (TV: The Woman Who Fell to Earth-The Power of the Doctor)
The Fifteenth Doctor frequently wore a double-breasted trenchcoat of burnt orange leather. (PROSE: "Heroes of Time" [+]Part of Whotopia: The Ultimate Guide to the Whoniverse, Loading...{"namedpart":"Heroes of Time","1":"Whotopia: The Ultimate Guide to the Whoniverse (reference book)"})
Worn by companions
Sarah Jane Smith occasionally wore trenchcoats. (TV: Eye of the Gorgon, The Last Sontaran, The Mark of the Berserker, et al.)
Amy Pond wore a dark teal trenchcoat during her encounter with Vincent van Gogh. (TV: Vincent and the Doctor)
Donna Noble wore a single-breasted trenchcoat of tan leather. (TV: Turn Left, The Stolen Earth/Journey's End)
Martha Jones wore a double-breasted trenchcoat of charcoal grey leather with her mauve tank top. (TV: Reset)
Susan Foreman wore a beige trenchcoat during her adventure on the Death Zone. (TV: The Five Doctors)
Worn by the Master
The Master wore trenchcoats in some incarnations.
The Bruce Master wore a black leather trenchcoat. (AUDIO: Faustian-Passion)
The Spy Master wore a double-breasted trenchcoat of black leather when posing as a Nazi in Paris. (TV: Spyfall) He also wore the Thirteenth Doctor's trenchcoat when processing her body as part of his master plan. (TV: The Power of the Doctor)
Worn by others
Detective Duggan wore a beige trenchcoat when he helped the Fourth Doctor and Romana II. (TV: City of Death)
Sally Sparrow wore a dark brown trenchcoat during her first encounter with Weeping Angels. (TV: Blink)
Vienna Salvatori wore leather trenchcoats done in navy, (AUDIO: The Shadow Heart-Vengeance) or black. (AUDIO: The Nemesis Express-Passion)
The Second Rani wore a black trenchcoat when posing as Professor Baxton. (AUDIO: The Rani Elite, Planet of the Rani)
One version of the Corsair with a bowler hat wore a black trenchcoat. (PROSE: Eleven Things You Probably Didn't Know About the Corsair)
