RE: What would you do if you seen a dog chaseing a deer?
I'd have done the same thing. I love animals in general, and I love my dog like a son (I don't have kids, so I don't know that FOR SURE, but I'm sure it's at least close), so I trained him well and I keep an eye on him when he's outside. He don't run. Whether it's a car or an arrow, if he gets killed because I let him out, it's my fault. If he bites somebody because I let him out, it's my fault. If he hurts or kills someone else's dog because I let him out, it's my fault. And if he got out on accident and did any of these things, it's still my fault. I'd still get the vet-bills, or the hospital bill, or the damaged property bills. In either senario, I have to pay the consequences. And if I let him run, I understand the consequences and accept them, when I decide I'm too lazy to train him not to run or don't keep him resticted from running.
Don't mean to sound so cold about it, but if you're going to let your dog out just to run the country, there's lots of ways for that animal to get into trouble, and it's not just his safety that should be considered. There's other people and animals in the world that he could hurt or that could hurt him. Coyotes kill a big number of domestic pets all around our area (N.E. Illinois) every year.
My 2-cents. Don't flame me for it. If you don't agree, keep your dog on a leash. We have leash-laws where I live. And this is one of the reasons.