Norfolk is a large, genuinely rural county with the Broads in the east and good, honest farmland across much of the rest, offering affordable grazing and a strong, unpretentious Pony Club and riding club culture. It is somewhat cut off by geography — there is no motorway through the county — which keeps land prices down but means real travel time for viewings and, for competing families, for reaching shows further afield.
Distances within the county itself can be substantial, so plan a day carefully if you want to see more than one or two ponies, and check journey times rather than assuming from the map. The upside of Norfolk's relative remoteness is value: a family budget goes further here than almost anywhere in the south-east, and the local pony community is friendly and used to newcomers relocating from more expensive counties.