This is the classic entitled rich idiot who builds a McMansion out in the sticks and has some vague idea that dogs "have the right to run." They are the reason country folk are suspicious of those who move from "the city." I can't tell you the job I had convincing my neighbors that I wasn't "one of those" when we bought our farm.
I am CERTAIN that, despite (because of) no leash law, there is a law that holds them strictly liable for any damage their dog does, and one that empowers you to kills the dog to protect your stock. (Not to mention your children.)
Nordic breeds are notoriously unreliable about (a) running away; and (b) killing livestock. Actually, strike that. They are very reliable about it. Most will do so every chance they get. It's unusual for a husky or Malamute to menace a person, and that worries me quite a bit.
I like keeping my dogs "free range." That's one of the thousand reasons why I chose breeds of dog who are inclined to stay home, and then TRAINED them to do so, and SUPERVISE them so they don't expand their home range.
Get online and find the relevant state and county laws about free-roaming dogs and livestock damage. Print 'em and have 'em ready.
Okay, I wouldn't want to kill anyone's dog either -- though I would have shot it when it menaced me on my own property. If you don't want to go there, get a paintball gun and pepper the bugger with red paint. Catch the dog and shave it. Actually, shave
part of it. Dye it hot pink. That often gets the owners' attention, and it doesn't harm the dog.
Or take the dog to the animal shelter/pound as a stray, which it is. Let the owners pay a hefty fine to redeem it. They're already probably paying a balloon mortgage on a 400 k trophy house, so I'm sure they can afford it.
And then convince
all the rest of your neighbors to join you in your poultry-keeping hobby.
I would put in a fence. It's not just one person's marauding dog you need to think about. It's your responsibility to contain YOUR animals, too.