I don't dog hunt so I really can't tell you, but I have friends that dog hunt, and I've never heard them say anything about this being a problem. There are a lot of guys here that do that, maybe someone like Rebel Hog can answer that for ya.
Man dog are great with infections and disease. I've had dogs that got snake bit, and were fine in a few days. I can't say that about how they deal with tires, my wife ran over my best dog, and he never did get over that.Neither did she.