I may be wrong, but I think that craman's reference to positive prescription may be a red herring. I think this applies to land ownership or usage (rights of way etc.) not to planning.
I believe that no enforcement action can be taken by the local planning authority against unauthorised development if such action is not started within four years of the completion of the development. The limit is ten years if the 'unauthorised' aspect is a breach of actual planning consent (eg. development larger than consent, or change of use not in accordance with permission etc.).
As far as your circumstances are concerned if your present stable were deemed to be a structure, it has already been there for four years so is safe. I would guess you could build a permanent structure on the same footprint but that or any further development would still need planning consent or for nobody to report it for four more years.
One potential problem is, however that mobile shelters and stables are marketed on the basis that they are portable and not fixed to the ground and therefore are not 'structures' and do not require planning permission. Many councils have taken action against these 'mobile' shelters on the grounds that although not fixed to the ground, they are nevertheless classed as structures subject to planning control.
In your shoes I would get some suitably rusty angle iron and bang a few bits into the ground and bolt them to the base structure of the shelter you could then claim that it wasn't mobile and was erected more than four years ago and therefore cannot be attacked. If your horse lady wants to add more mobile stables at her own expense even if there were to be any come-back from the neighbours, the worst that could happen would be for those new stables to have to be removed.