Most of us assume that our domestic horses will spook and try to run if they see a predator.
This is not always the case. I was riding in Wyoming when my horse tensed. Down in the valley was a wolf. Wolves, working in a pack, can certainly bring down a horse, especially one that is injured. Needless to say, my horse was not happy.
She did not, however, spook.
It's actually simple. Spooking is a reaction to the possibility that there is a predator about to ambush a horse. This is why some horses don't like going into water that has trees above it - classic ambush situation.
My horse tensed. She looked at the wolf. She assessed the wolf's body language, and she realized - much faster than I did - two things about this wolf:
1. The wolf was currently alone, away from her pack. A single wolf is no threat to a herd of horses.
2. The wolf had something in her mouth. That something was wolf colored and squirming! It wasn't a prey animal - it was one of her cubs. Female wolves often move their young cubs from one den to another for safety.
My horse's mental process went "Predator. Alert." But because she could clearly see the wolf, her mind then went "Wolf alone, not threat. Wolf mom with baby, definitely not threat." That wolf wasn't hunting - and she knew it. So, while she was very aware of the wolf and watching it, she did not have any need to run.
This, of course, is the origin of the horse's almost uncanny ability to read our body language.