COVID is known to be carried by a number of different mammals, both domestic and wild. In response to the USDA finding COVID in deer in other states, in the Midwest and Northeast, Oklahoma blood samples were sent in for analysis. These samples were from the routine Herd Health Studies in 2020 and 2021, and some did return positive for SARS-CoV-2.
At this time, we do not know how deer contract the virus, but we do know that all of us (vaccinated and unvaccinated) are a potential source of infection to other species.
Currently, there are no documented cases of humans becoming infected from whitetail deer. At present there is no known risk of COVID exposure associated with cleaning deer or eating cooked venison. However, when handling deer or other game, individuals are in contact with an animal of unknown COVID infection status.
The risk of COVID infection when handling harvested deer can be reduced by following the same guidelines recommended to reduce human-to-human transmission (hand washing, gloves and masks). Likewise the risk of severe or fatal COVID-19 can be greatly reduced through personal vaccination.
For more information on COVID-19 and pets see the CDC information here: https://www.cdc.gov/healthypets/covid-19/pets.html