I also highly recommend the thread that Romy posted. There are so many ways to initiate an interaction, but I think they are all about finding a common language. That process takes time.
The way I see "just being with your horse", is not just being with my horse at any place, but at HIS place
. I meet the horse at his home, in the herd. And there, I behave by their rules, trying to blend in with their customs. If I remember correctly, I wrote about that in more detail in the aforementioned thread...
Regarding playing with horses, I think horses are in generally curious by nature, but they are also wary by nature. As I experience it, playfulness comes out only against a backdrop of safety and all games need established rules at first. That applies especially to playing with objects.
With Mucki, it took a long, long time to have him play with me when we are alone in the arena. At first, I mostly met him in his home, among his herd buddies, in the environment where he felt absolutely safe. Even there, it initially took a while for him to engage in playful interaction with me.
Then, in the beginning, I spent most of the time playing, but the playing was actually a means to find a mutual language together. I learned how to use my body language so that Mucki could understand it, and Mucki learned what I meant by certain cues that were not so intuitive.
From that common ground, we were able to have fun with other games, like playing with a ball for example. But I had to explain to Mucki that objects (that were uninteresting, or even scary before) could be used as toys.