It wouldn't hurt to be soaking her hay as well, especially if it is this seasons hay, it can contain sugars etc. Try soaking it for a few hours, and when you pull it out, you will most likely see water that has turned beer coloured, and smells like a brewery. I have a miniature, and she was grossly obese when she arrived here looking like this:
Now she looks like this
You could take her for runs up the road or through the paddocks (provided the roads have a grass verge) I'm unable to run much because of my back, so I get on my sisters little 100cc motorbike and go up the road with Gemma like that, she absolutely loves it and just wants to keep going.
Could you attach tyres to her when you ground drive, even if she is only driving at a walk it will still help some