It will be interesting to hear where the OP is now with her friend and the ‘training’. She’s had a few days for a conversation.
OP, part of life is that relationships change over time. Sometimes you have to establish boundaries, push back on someone who is being a bit pushy. You can’t keep everyone’s feelings the same all of the time, because there will always be factors on both sides that change things.
From your post I can tell that you are feeling increasingly uncomfortable with your friend, because of your friend’s actions. So doing nothing won’t save the friendship because your feelings are changing.
You have already asked her for change, and she is not respecting your request. She is taking control of something that is yours - both your horse, and your preference for how your horse is handled.
When you ask her to stop, you have to take back that control. If she’s someone who prefers to be the boss then it will be a bit tough. But at this point if you don’t take control back, you are effectively giving the horse to her to do as she wishes.
And there is no point in trying to convince your friend that her methods are not right for this horse. That’s not the basis for your discussion with her. You are telling her that it’s your horse (or else that you have the primary responsibility for the horse) and this change is your decision. If you think that she won’t take that kindly, then she’s not a great friend. A good friend will respect your feelings above her whims toward your horse.
A little bit of distance between you now may help establish a better footing for your friendship in the future, when you initiate more cordial communications again.
Also … if she is defying your request now, you may have to remove from her access anything of yours that she is using. Is she using her equipment or yours? If yours, put it in your car and keep it there until this is sorted out. Because she has already shown that she does not respect boundaries and your wishes, so you need to establish some physical boundaries as well.
The other point is – have you SEEN what she does each time she works with the horse? Your post #1 is interpreting what must be going on based on the horse’s behavior. But that isn’t the firmest ground for discussing this with your friend.
So I would ASK your friend first what she is doing with the horse, and see what she has to say. And/or, be out there when she is and see for yourself what she does. Only then would I know definitely what she is doing with training.
I have to agree with previous posters that, assuming your friend is changing the horse’s behavior, it seems unnecessary with such an established horse. It could be that your friend is anxious to use her training techniques on some horse, and yours is available, so that’s why she’s doing what she’s doing.
