Thanks for your question.
It would depend on whether the paddock is within the definition of the property which has the benefit of the easement.
Do you have a pdf of the title so I can check?
Thanks for the copy transfer. Do I assume correct that you own/are buying the red land?
The relevant right for the neighbour and the right of way/access is at paragraph 3, second schedule. Do note para 2, fourth schedule. This allows equestrian / ancillary business and commercial use.
The easement will pass with the land so a buyer of the retained land will get the benefit of the easement, even if part of the retained land is sold. Furthermore, I think that the easement can also be used for ancillary equestrian / commercial use.