According to their website, the NT have two herds of Exmoor ponies on the White Cliffs:
http://www.nationaltrust.org.uk/white-cliffs-dover/wildlife/view-page/item884329/
There is a lot of concern being expressed on Facebook that some horses are going to be put down at the end of the month. Are these the two you are referring to above, Vic?
(Quote)..... apparently one has already been shot in full view of the other two! The elderly man that regularly gives them treats is very distraught that the other two are being shot at the end of the month and is trying hard to get support to prevent this.
(Quote).......On another site someone has written that one pony is unwell and has to be shot and the other cannot be introduced to other ponies (no idea if that's true). Very sad if this is all true.