A deer was a quadrupedal mammal native to Earth, a young deer was known as a fawn. They usually inhabited forests, and were herbivores. Sometimes they were used for sacrifices to a god. (TOS: "Who Mourns for Adonais?")
In 1957, when a team of Vulcans crash-landed on Earth, their scanners detected the life signs of two deer approaching. Upon seeing the deer, T'Mir commented "Fascinating." As they hadn't eaten in several days, Mestral considered capturing one and eating it, as it could sustain them for several days. However, Stron was disgusted at the thought of eating meat, calling it "savagery". (ENT: "Carbon Creek")
While criticizing the furnishings of Lieutenant Uhura's quarters in 2268, Elaan, the Dohlman of Elas asked "Am I a soft Troyian fawn to need pillows to sit on?" (TOS: "Elaan of Troyius")
In 2000, Alexandria Books had a Christmas ornament on one shelf that looked like a reindeer pulling a sleigh. (VOY: "11:59")
A deer appeared in Commander Chakotay's akoonah-induced dreams. He was hunting the deer through USS Voyager's corridors with a spear. In the ship's mess hall, the deer morphed into a member of the dream species. (VOY: "Waking Moments")