I watched most of the free play video, not all.
It's obvious that you two have a very good relationship. I couldn't get my horse to do that, no way. I need a round pen to keep him. He'd head out to the herd if I was in the open with him.
Your mare likes you, so she chooses to stay with you.
I liked pretty much all of what I saw. A couple of minor things:
A few times she got kind of close on you and had her shoulder kind of bent into you. Not so much being aggressive, but a bit overly familiar and cuddly for me, But the video isn't that clear, so the actual distance between you two is hard to estimate.
When you were playing with her and she was following you, there were times when you made changes that were kind of abrupt. That isn't always such a bad thing, especially if her attention is wandering. But you can make it a smoother dance if you use the shifting fore and aft of the upper body as a precue to the change that is coming in your feet (stop/start). She will really cue into that shift of your weight through the upper body and be more ready to stop, than be surprised by it.
When you turn right or left, you can bend your body in the direction of your movement and it kind of "sucks" her along. So, for example, if you are facing her and you want to suck her to back up, you bend your abdomin away from her and step backward. pushing her away from you, push your abdomin into her and stand up straighter.
Try running with her and exaggerating your high steps, see if she will copy you and Piafe or Passage next to you. maybe she can be taught to Spanish walk next to you. People do it, though don't ask me how the do it.
Also, don't just have her follow you. Once you feel your connection is good and she is followoing well, try moving her away from you and then trying to draw her right back. So, move her shoulders away, but then step back and draw her back , then turn that into a change of direction or a half circle.
Practice pushing her just enough backward so that you see her shift her weight onto her back feet, but NOT step backward. Then when she is weighted on her back feet, ask her to step her outside forefoot over then the inside fore over. Turn on the haunches.
Work in this way, having her weight her hind end in preperation for unweighting the front will be really beneficial when you are under saddle.
That's all I can think of. You are just an adorable pair and a lot of fun to watch. Looks cold!