In many areas the deer are over populated and that makes the spread of disease easier. Also more malnutrition, getting hit by cars etc.
One case I read of a large park that had about 3 times the carrying capacity of deer due to a few years of really good food supply and the lack of predators. The park people wanted to have a special hunt to thin the herd by at least 50% but the Nature Extremists brought political pressure and killed the idea. Then the cycle of abundant food years ended and over a three year period malnutrition, starvation and more than one disease killed over 90% of the deer in the park. And their deaths were a hell of a lot worse than being shot and becoming food. Plus many of the remaining deer actually had to be trapped and euthanized by wildlife department veterinarians since they were now disease carriers and in poor health to the point of suffering. Over the last year or so I keep seeing "trail cam" photos of diseased deer in many places around the country on the net - it is happening again and in more places.

In re natural selection in virus mutations - a lot of experts believe that the literally hundreds of viruses that cause the common cold around the world were all like Covid and its relatives at some point in history.
Hey Folks, History Teacher Here - History is more than your memory or even your school history book! It goes back millions/billions of years and even for humans and our near relatives it is over a million. Not just to your birthday.

The virus has spread to a number of different wild animals species, and that is in line with how it spread from animals to humans in the first place (as in there was no need for it to have been engineered in a lab, btw). That it is widespread in deer is concerning, of course, especially since it could also jump to livestock and so into our main food supply. I have no idea if that will be dangerous or not.
As for risks from being out in nature where there are deer -- it should be safe so long as you don't pet the wildlife. I don't know about hunting or eating them.
We will probably never be rid of this damn thing, but that would be the case even if it never jumped back to animals from humans. As this virus changes, it is reasonable to hope that it evolves to become more and more benign. There is a tendency for natural selection in viruses to work in that direction because it is of the greatest benefit for the virus. But this will take time.