Callimachus, in "Hymn III: To Artemis" describes deer being used to draw a chariot.
Callimachus, "Hymn III: To Artemis," in Callimachus: The Hymns, trans. Susan A. Stephens (New York: Oxford University Press, 2015), 118-19
(95) fawns and the hare that does not close its eyes, and at sniffing out the covert of the stag and where are the lairs of the porcupine, and at following the track of the roe deer. Leaving there (and your hounds hurried after), you found at the foot of Mt. Parrhasius (100) bounding deer—a great business! They always grazed by the banks of the swift current with its black pebbles, more massive than bulls, and gold flashed out from their horns. You were amazed and spoke to your heart: “This would be a first hunt worthy of Artemis.” (105) There were five in all. Four you took by running swiftly without hunting with your hounds, so they might pull your swift chariot. But the one that fled beyond the river Celadon through Hera’s command, so that it might later become a test for Heracles, the Cerynian crag received.
The translator, Susan S. Stephens, adds a note to the above:
πίσυρας: Aeolic for τέσσαρες; it occurs occasionally in Homer (Od. 5.70, 16.249). Of the five deer, Artemis takes four for her chariot, leaving the last to be a labor for Heracles. The capture of the Cerynian deer was the third (or sometimes the fourth) of Heracles’ twelve labors. Treated in Pi. Ol. 3.25–30 and Eur. HF 375–79, it was also a frequent subject for the plastic arts. Reference to this event here may serve as a temporal marker—this is very early in Artemis’ career. At some future time the divinity will encounter the deified Heracles on Olympus. (Ibid., 135n105)