The Definitive Map
The Definitive Map is the map prepared by a surveying authority (County Council) which is a legal record of the public's rights of way in one of four categories (footpath, bridleway, or byway open to all traffic).
If a way is shown on the map, then that is legal, or conclusive, evidence that the public had those rights along the way at the relevant date of the map (and has them still, unless there has been a legally authorised change).
But the reverse is not true. So the showing of a way as a footpath does not prove that there are not, for example, additional unrecorded rights for horse-riders to use the way. Nor is the fact that a way is omitted from the definitive map proof that the public has no rights over it.
It is often said that it is "illegal" to ride a horse on a footpath. If a footpath path has always been ridden there could be a right of way (albeit unrecorded) for you to ride the path.
The only offence possibly committed is Civil Trespass unless there is a specific local bylaw or unless you unlock or remove gates or fence which is Criminal Damage.
If you are stopped from using a path by a landowner, always respect the wishes of the landowner. If in these circumstances you believe you may have right to use path you must consider sumitting an application for a Modification Order (if the path is not already recorded as a brileway or byway),