I have seen empathy in action with our horses.
A few instances...
We had a blind horse come in. Some of the other horses shunned him, which was natural- after all, a disabled animal slows down the herd, leaving them vulnerable to predators. We had a pony at the time who took a liking to the blind horse. The pony would guide the blind horse around the pasture, to the point that the blind horse would rest his nose on the pony's rump and be led around. We put a little bell on the pony's halter so the blind horse could hear him and follow him. Now, tell me, is that not empathy?
Last year we had a llama give birth, and her cria was killed and half eaten by a cougar. She grieved at the site where the cria was killed for several days, refusing to leave, eat or drink. We brought buckets of water to her in an effort to drink. Our vet said if she didn't come out of the grief, she would die. The next morning several of us witnessed an old mare go over to the llama, stand side by side with her for several hours. The old mare previously had never showed an interest in the llamas. They stood together like this, heads down, leaning on each other. Finally, the mare nudged the llama gently and then they both started walking back to the hay. Llama proceeded to eat, and recovered. Now, why should an old horse who didn't care about that grieving llama bother to go over and obviously comfort her? In my mind, she acknowledged the llama's grief, comforted her and encouraged her. That is empathy.
I don't know how many times I wasn't feeling good because of my chemotherapy and I would just go out and sit on the grass with my horses grazing around me. On more than one occasion I had a horse come up to me, lay her head on my shoulder and comfort me.
Horses are a wealth of emotion.
Spent a whole hour today laying in a pasture, waiting for a sparkling vampire to show up. Alas, I woke up and looked over, only to find a mound of horse crap. Sigh.