Do horses dream?

I read that question in a book today called "Frag Monty" (In English, "Ask Monty" (Roberts)).

I can answer this! I've had two experiences with my horse that seem to point to "Yes, horses dream."

Monty related a second-hand story in his book, which was actually quite interesting. It was about a farrier who worked on a horse that was so relaxed, it fell asleep. Suddenly the horse woke up, and very uncharacteristically fruck out, kicking the farrier. No one would believe this gentle horse would harm a person, and the farrier said, "I haven't the slightest doubt that I disturbed the horse as he dreamt of a lion." (If my translation from the german is right) Hm. I can tell one like that!

Never do this. Never, ever, ever climb under a fence at night to check on your horse, if it is too dark to see your horse. I did this at an endurance ride late at night. I couldn't see my grey horse it was so dark out. I crawled under the paddock wire, and suddenly heard hoofbeats galloping away and felt blood coming out of my head. I required stitches that night. I knew my Baasha would never kick me intentionally. He must have been in a deep sleep (after a 50 mile ride) and I must have been a mountain lion crawling toward him in his dream.

My second horse dreaming experience was much nicer. I was camped at an orienteering ride with Baasha, in a lovely private spot with nothing but my horse and me, surrounded by trees. I had Baasha highlined and I made a fire near him. As the hours passed with me sitting in front of my fire, he eventually lay down. Later he stretched out in deep sleep on the other side of my fire. Then he started dreaming. He must have been dreaming of running, because that's what his legs did. I was totally astonished. Horses dream! Mine dreams of running!

I told everyone in the morning but I'm not sure they believed me. Who has ever heard of a horse dreaming like this? (The picture is one of Baasha's last endurance races, and you can see clearly the "spongeline" of cleanliness, ha!)