A few years ago ,a farmer close by here, went to his barn to take care of his sheep. He went into the barn and found a coyote about like what you have there. He said it was in with his sheep but not bothering them at all, just wanted to stay warm. He promptly killed it.
I have seen what mange does to a pack of black and tan coonhounds as well as domestic hog's, it used to be really hard to stop, I hope it's easier now.