Autumn's the season when the free-living ponies on Exmoor are rounded up, inspected and the foals are branded to identify them. Each Exmoor pony herd has a different mark (for example, the Winsford herd's is an anchor). All the ponies have an owner and all are registered with the Exmoor Pony Society which, among other things, monitors and safeguards the ponies' gene pool (Exmoor ponies are listed as an endangered species). Amazing to think that these small horses are, in effect, prehistoric animals; sturdy and very well adapted to a moorland climate, they haven't needed to evolve any more.
The nearest herds to Exmoor House and Wheddon Cross roam around the Dunkery Beacon area, so you may well see ponies if you're walking up on Dunkery Hill. They seem happy to pose for photographs, but don't annoy them by trying to get too close, especially if they have foals with them.
You can learn more, and ride one of the ponies, at the Exmoor Pony Centre, near Dulverton, run by the Moorland Mousie Trust (it's necessary to book in advance to visit the centre because parking is limited).