The specific White tailed deer (Odocoileus virginianus) subspecies they have at Oklahoma City Zoo is a Texas white tailed deer (Odocoileus virginianus texanus)
As numerous as they are in the U.S. most larger zoo do not keep them as they would be seen as a waste of space. The only places you find them now are at smaller zoos. They also have become very popular as private pets. I know multiple people who own or have owned white tailed deer as pets. They say that the deer would act like a dogs and become loving pets.
From what I am reading on Zootierliste, 7 collections in Europe currently keep White tailed deer (Odocoileus virginianus)
5 collections out of those 7 list their White tailed deer (Odocoileus virginianus) as being of a particular subspecies, the White tailed deer (Odocoileus virginianus) subspecies they have at those places is the Northern white tailed deer (Odocoileus virginianus virginianus)
As I have said above, the other 2 places list their White tailed deer (Odocoileus virginianus) as having no subspecific status. Looking at the list of other white tailed deer subspecies having been imported into Europe, it appears that there are no records of Texas white tailed deer (Odocoileus virginianus texanus) ever being in Europe, so I doubt that the white tailed deer at those 2 places have any Odocoileus virginianus texanus blood in them, so in that regard the people in the Oklahoma City area average person and zoo enthusiast alike dont really realize how luck they are...