The advantage of a lens with long range ability is that one can achieve an appearance of closeness with a minimal risk to the photographer but with a maximum of respect to wildlife. That being said, Nature has her own rules & one should never be complacent when photographing any animal at any distance.
Just like people, each one is an individual with a unique personality & history. And again, just like people, they can have bad days & good days, depending upon food sources, encounters with rivals or even day to day offspring rearing.
Sometimes opportunities can arise where you can obtain glimpses into the daily routine of wildlife, which might seem mundane in the human world but in the natural world, because those moments occur generally without a witness, can be a window into wildlife's private lives.
And if you look closely at the coyote's left front paw (right of screen) (Photo #3 & 4), there appears to be a small injury to the top of the foot. I did notice some intermittent limping as she crossed the snow, not too serious though. It looks as if the injury is around a toe or nail and not to the actual pad of the foot. Nature's natural healing powers are amazing & hopefully this will soon heal. In the interim, she definitely had no difficulty in trotting or even running through the snow.