What do you regard as a heath. I regard it as rabbit country, with poor soil and lots of gorse bushes everywhere. Something like this:
That is how it seemed to me to be described in the book. You cannot grow crops on it because the soil is too poor. Sounds like you can't even graze sheep on it because there is not actually much grass. I do not think a heath is the same as a moor because it need not be high up or particularly hilly. I don't think the land was very productive, economically speaking. Cutting furze or turf for fuel does not sound very remunerative. I wondered whether anyone owned those heath-cropper ponies or whether they were wild. What do they eat? If you cannot graze sheep on the land, then how can ponies survive?
I watched a YouTube promo clip on the TV series of Return of the Native with Catherine Zeta Jones. One thing that bothers me about it is that it was filmed on Exmoor. Exmoor is not a heath, it's a moor.