Today, we had a family thing at my aunt's house, aka where my horses are. As the family was having dinner I did my usual thing - I rode. I decided to get on the barreling mare who never seems to run out of energy..it's not that she's bad or anything, just loves to run. We walked a few laps, trotted a couple then I let her run. After a while I dropped the reins and let her do as she pleased, not in an unsafe manner, she's very sane. After a couple times of her running, she saw that it was much nicer to walk. She walked a couple times, and to my surprise actually dropped her head. We've had her for 4 or 5 years now [I lost count, but I believe it's 4] and she hasnt really relaxed like this with someone on her back. Even more shockingly, she left it down. She has ALWAYS moved with her head held high.
So the lesson I learned is, give a horse the opportunity to do what they want, and they may just do what you want instead.