The new, cow-proof fencing was installed around a much larger area than the current garden. This was done so that we won't need to re-fence again when (if) we decide to expand the size of the garden in the future.
The older fencing which goes right around the edges of the garden will remain in place. Even though it has been pretty mangled by the cows, it still keeps the dogs out of the garden, something the new fence can't do. I suppose sometime in the future we'll attach mesh fencing to the cow-proof fence, so that it can be both cow-proof and dog-proof.
There's the gate - site of many a broken fingernail! It's not Trish-proof, but it is certainly Trish-resistant.