Sorry, not answering your question directly, but when I fostered the pony from the RSPCA, I went straight to the rehoming centre on one of their regular open to the public days, and took it from there.
I'd turn up in person as soon as you can, have a look round, and get known to them .
You will see so many horses and ponies there you will want to take them all home! I went for one, couldn't get another out of my mind, so she came home a few months after the first