You'd have to look on the DEFRA website as I'm sure that the Laws on ragwort growing in grazing pastures now relates to horses aswell. I believe that the landowner is the one who would be proscecuted.
This is all by the by though - as a livery with horses grazing in a field with ragwort why wouldn't the horse-owner want to eradicate the ragwort anyway? I sure as heck would.
I have two acres which I am desperately trying to keep ragwort free but it's springing up elsewhere as soon as I've dug up a batch.
Next door is 10 yes 10 acres of wall to wall ragwort plus an elderly pony and a young shire mare.
The landowner is an absentee landlord with her own private yard and the horse owner doesn't care. The BHS welfare officer following a complaint went out to the horses but did not want to get involved so accepted the owners waffle and left.
On the other side of my fence line is a hedge of ragwort about which I can do nothing, I do not now where the land owner lives, what her name is or any relevent details now what?