Carol,
Glad to hear,no horses on tables!
What about lighting? Everything out doors? What about clouds,sun,clouds, and different exposures of the horse and work,will that look ok to your client. Can't see doing 200 shots,with horses involved in 2 days,unless very long days,then I would price it that way.
Even only charging $10/shot which is cheap, leaves you with a nice project,which comes out to $1,000/day rate. I would ask for at least 1/3 up front,half would be better. And then the balance upon delivery/acceptance of the images. Make sure that this client has a very good sense of what images she wants and doesn't throw something in that is beyond this job, or your experience. 2 days still sounds a bit short for 200 images and live animals.
I would bill the 2 days,say $1,000/day, with a $500 fee for post production of those images. There will be a LOT of editing, to get to the final 200 and even $500 may not cover this work.
If she seems reluctant to an advance, then I would be concerned about the rest of it, from paying you to publication of the book.
I would also ask,in the contract, for full credit for this project's images and maybe even a small bio and link,at the back of the book,you never know where this may go!
Rich