I don't know for sure, if they handle deer different. But typically any time you put in a claim, it leads to the possibility of rate increases. Also increased rates based on where you live.
On the other hand, I am tired of hitting deer, or the brakes. So I am a little different than some sportsman. I don't care if you go out for 10 minutes and don't get a deer. Same goes for wolves. I want to manage them, and want them less bold, but I still want them around to eat deer.
Personally I think many hunters have a list of excuses for why they didn't get a deer, but don't look at themselves.