from what I heard
1) Snares work wonders
2) if you love your pets, keep them home in a pen or tied up.
3) dog(s) and wolves will kill 20 - 30 sheep and not eat a single one. You'll spend the next hour; shooting the animals that have been hamstringed, gutted, wounded beyond healing. Most people don't understand DNA and years of crossbreeding for your perfect animal can be reduced in minutes.
4) Never feel bad, see rule #2
5) dogs love to chase horses through fences (barbed wire will rack up a quick vet bill). Some livestock won't take crap from 1 dog, they don't stand a chance against 2 or more dogs.
6) dogs and wolves will reduce your calf heard pretty quick. Coyotes have eaten calves as they are coming out of the birth canal. Cow can't do crap; since it's hips are locked up.
7) coyotes, wolves and dogs love snow with a hard crust. They'll run a healthy deer, sheep, Elk to exhaustion and then kill it. Predator runs on the crust while the said victim breaks through the snow. Sad thing to watch.
I snared quite a few coyotes here a few years back when I went after them with a vengeance. Unfortunately I got a couple around the body (I was a newb) and I'm sure they suffered before expiring (I check traps daily).
I stopped when I got of all things a yearling deer that had tried to shimmy under a five-strand barb-wire fence.
I still trap a lot of raccoons out here, but I just shoot the coyotes.