Look, I have sympathy for your loss, but as a stockman here in the western U.S., I have a different take of the situation. First, you say your neighbors shot them while they were lost in a snow storm... it's been my experience over several years, that dogs rarely ever 'get lost', especially in a snow storm. Secondly, what were they doing loose?
If you ever cleaned up a field littered with dead and dying sheep (or claves, in our case), with their throats ripped out, guts lying in a trail behind them or the side of a head chewed away while the animal lives, you too, might have a differing opinion of the various and sundry 'pets' that track all the way out from town just to have fun reverting to their predator/prey DNA and chase anything that runs from them.
I've shot several 'pets' ranging from family cherished German Shepherds to smallish terrier types, that were several miles from their homes. Some farther than others. Fact is, it simply points up the owners lack of caring and watching after a pet.
Of course, when I inform the owner (if I can identify them) there's the typical outrage, until you present them with the bill for dead and dying animals. I have little or no hope of collecting, but it brings their outrage to a sudden and silent end... they're happy to see me go.
I'm sorry for your loss, but hope its a lesson well learned. I'll hide and watch while the outrage bubbles over amongst the readers...