That's really interesting! I always heard moose could be dangerous but maybe that's in rutting season (pretty much any males are dangerous then).
Our foxes and coyotes regularly kill livestock so there are government agencies that enlist hunters to bring in a number of hides when culling is necessary. There's nothing like KICKING a hawk OFF a chicken (one tried to nab one right next to me when I was little -- the chicken and I won).
We have mountain lions and bears but those are RARE, more likely bobcats (known as lynx in some areas), coyotes, possums and coons kill off your critters. Owls and hawks, do, too, but you can protect the smaller livestock easier than the large ones that range freely.