Hi Anne Marie,
yes, it is really fun to watch them.
About your question, what I am doing in the background:
When watching horses, one can notice, that if one horse feels like playing, it will go and ask the other horse(s) to join in. Then, when they have been running, rearing, bucking, etc. for a while, they will take a break and just graze or groom. These breaks are like saying "hey, this is no fight but just for fun, we are all friends and playing" (at least that is how I interpret it). Then one of them can start the game all over again until they are satisfied.
So, I try to imitate this. You can see, that I do not have a flag, whip or "tiger" nor food rewards, but I raise my own energy up, then go and ask for play. By raising my own energy, when I do it well, the horse catches on.
The breaks of just "grazing" together I did cut out for the video, they might be bit boring - for most people anyway.
In the first video you can see both horses running out once and then returning. At that point I went to check with the cameraman, if he was still warm enough, or wanted to leave. After that, I just stood watching for a while - the horses had lots enough of life and fun on their own.
Then I started to lower my own energy and call for a break by that - doing as if grazing and breathing like after having had a good run. The horses did follow that example and soon afterward took a roll, what feels always especially good after running.
Before I was able to play like this, first I did watch how the horses do it among each other, then I did lots of asking for play, or joining in with their play. In the beginning they looked somewhat puzzled at me.
But now they know that one can also play with people - we are still exploring on that. I think they now try to find out, how to ask me politely for playing.
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And she is getting more and more playful 
) and then repost.
On most there was not much sound in the first place and I did not edit all videos, but now I have again something to figure out with the video-technique. 
