Might as well shoot his horse too if he has one. Surely yall wouldnt shoot a mans dog. Talk to the owner. Now if it was agressive towards a human thats a different story. As far as deer I bet that dog didnt mess anything up anyway as long as he was just passing through.
I'd hate to, but dangit, keep your dogs in a fence or in the house! Never seen anyone let a horse out to roam.
Let's just say you have a 16 year old daughter, or kid that loves animals. Dogs especially. This dog runs out in front of their car and they swerve to miss it, and the worst thing happens. What now? It's not just about messing up a hunt. I know that situation may be far fetched, but crazier things have happened. Put a fence up and don't worry about it.