I used to be a cold hearted, ruthless person when it came to dogs running loose through our cows. And November through May we have 600-700 head of critters within 2 miles of a rez town so I get quite a bit of interactions.
But I learned that 90% of the time the dog(s) won't cause any trouble.
Chase 'em off with the pickup and shoot a few shots in the dirt, that's generally enough to keep 'em away. Anymore I really dislike shooting anything much less a stupid dog.
Almost shot this rascal when she was tearing around our little feed yard barking at the calves.
Now she's our best buddy.