It would only take a handful of transmissions to a community to have something like COVID spread like wildfire through the deer population. They may not interact with humans much, but only one carrier could infect several others and then that cascades to the entire population. Deer don't get vaccinated and don't wear masks.

The good news is that even if COVID is running rampant through the deer populations they shouldn't pass them on to humans very often, so if humans are good at identifying and stopping isolated outbreaks then we can live with the risk.