Hi Enzo:
Circe and I have been doing this exploring while hand walking, not while riding. (She's still young and I'm just starting to introduce her to having me on her back.)
And my suggestion would be to start this from the ground with Karexa, first, even though you two have done lots of riding together.
Part of the goal of this particular game is to give up as much control as you can force yourself to do!
And I think that's much harder if we're sitting on them than if we're standing beside them. (I even had to physically let go of the lead rope for a while because my impatience was so strong and I'd get bored and want to do something else, and then I'd find myself dragging her around again.)
In terms of Karexa just stopping at a patch of grass and grazing for hours -- the first few times I did this with Circe, she stopped and grazed for quite a while. That's okay if that's what she wants to do!
This was great for both Circe and me when she was spending a lot of time grazing -- I had to let go of my instinct to go "DO!!!" something, and she got to be outside doing what she loves doing more than anything else...eating!
Romy has found a very sophisticated way, I think, to work through when grazing is okay and when it isn't for her horses, but at least to start, I wouldn't worry about it.
I discovered that Circe liked to graze, but she also got bored with it fairly quickly and wanted to do other things. And for the first several days we did this together, it was absolutely her decision about when she wanted to move on from that particular patch of grass. But, once she'd realized that she could eat when she wanted to, if I pointed out something else that looked like it might be interesting, she was very willing to go take a look at it. (When I did this, I would just point to it and talk about it -- if she was interested, we'd go look at it -- but I never made the decision for her.)
I guess my best advice to you is to experiment with Karexa! If she is really stall bound, the first couple of times you do this she may not want to go anywhere. That's okay! A lot of this is about learning to trust their speed and desires. I'm guessing that she will eventually decide it's worth going exploring if you're patient.
But, if nothing happens for several days and you feel stuck there, you might experiment with putting some hay down out side of her stall where she can see it and let her decide if she wants to walk and go eat it.
Why is it, do you think, that she doesn't want to be outside and would rather be in her box?
Is it fear? Is it her belief that she isn't going to have fun when she comes out? That being out means being worked with no play? Something else?
You and she will know and/or find the answers to this -- and how you approach this together should be about those answers, and how you can help her to see going out as pleasurable.
I don't think there is any one way to do this -- the only key, for me, is invite your horse to be the leader. This may take some time itself, too! Circe, my filly, was so relieved that I'd finally understood her desire to make decisions that she was happy to make them instantly. My other horse, Stardust, who comes from a difficult background and got taught not to have opinions, was less sure if it would be okay for him to take the lead, and it took us a while for him to trust that I really meant it. But he did finally believe me, and he began to open up in a way I never thought possible.
With your background in medicine, it might be really interesting for you to think of the first steps of this as a diagnostic tool for both of you first -- what happens when you step back from being in charge? What happens in her body, mind, and heart, and what happens in yours? You're doing the preliminary questioning about a case -- not jumping to conclusions about what it might be, not rushing in to provide treatment, but are listening to the patient and the symptoms as carefully as you can -- and in this case, you're both the patients!
This process is, for me, about exploring, not achieving, if that makes sense. It's not possible for a horse to make a mistake -- whatever she wants to do is the right thing, even if that is just going home at first (or staying at home). As you do it, if my experience is any indication, her interest in the world will continue to expand -- if it's her decision to explore it.
For me, this has been one of the most rewarding things I've learned to do with my horses, and also the hardest. It's not easy to keep myself from being the one making the decisions! And we don't always do everything that they want to do, now. But I have learned so much by continuing to work at this, and try to remember to make sure to spend time letting them decide for themselves every week. When I remember to do this regularly, they are much more willing to take my suggestions at other times.
Hope this is helpful!
All the best,
Leigh