I think you probably need to establish who's responsible for the boundary fence in question. If you have any paperwork relating to your property, the boundary ownership/responsibility might be shown like this:
which means that whoever owns the land above the line is the "owner" of the boundary. If the "T" were upside down and below the line, the owner of the land below the line would be responsible. In other words, whoever owns the land on which the "T" lies is responsible for the associated boundary.
Sometimes things get a bit complicated. For example, it's often the case that in a road with a row/line of properties, each property-owner is responsible for two of the rear boundaries. One way of explaining this is that if the rear garden is a simple rectangular shape, the owner would be responsible for two of the boundaries e.g. left-hand side and rear (imagine "L" upside down). It's best not to to assume ownership of a boundary because sometimes "boundary" can equare to "minefield".
Of course things aren't always clear-cut! However, what you can do (if you've got enough room) is create another fence inside the existing boundary, and attach some horse-deterrent electric fence-type gadget. In this case you'd need something like a car battery in a waterproof container, if it's too far away to connect to the mains electricity supply. I think I mentioned in my earlier post that it's probably best to go and get some ideas/advice from a local agricultural supplier/merchant. A bit of googling beforehand will probably help too!