Deer are animals in Thief, though not seen alive in any of the Thief games. What is seen, however, is Deer Legs, which seem to be a lot more common than Cow meat.
In the first TG cutscene, the wide painting on Constantine's mantle shows people fleeing from a herd of enormous antlered creatures. In T2, a small carving on Gervaisius' desk depicting an adult male mule deer is seen in the mission briefing for Casing the Joint.
Deer skull standards are often placed outside Pagan sanctuaries in TDS.
Behind the scenes[]
Deer trophy in the Thief 3 Editor
In Thief 3 Editor, there is an unskinned, static mesh of an unused deer trophy.
An easter egg near the end of the credits for TDP and TG, a drawing in imitation of Constantine's depicts a huge bipedal antlered creature piloting a flying saucer. This could represent the Trickster, or perhaps some unknown Chaos Beast.