The fence isn't really suitable anyway as it is. Too gappy. Plants would just fall through to the other side too. It also doesn't look very high, so the problem described by @Dovefromabove would exacerbate it.
I'd put a hawthorn hedge in there if it was mine. A reasonable distance in from the fence so that it could establish, even if there's stock on the other side. We're almost at bare root hedging time, so it's a more economical way of doing it too. It will also provide some shelter from wind if you have any there. It seems quite exposed.If you wanted, at a later date, you could add a climber to grow through it too.