Dorset has a proper family-pony pedigree — it borders the New Forest and Hampshire, and the same chalk downland and hunting culture that makes the wider region strong for ponies runs through it too. It is Thomas Hardy country: rolling, genuinely rural, with a strong Pony Club and hunting tradition and good, honest grazing on chalk downland rather than heavy clay.
The coast brings its own culture, with some ponies used to sandy or exposed grazing near the Jurassic Coast, while inland Dorset is classic downland hunting country. It is a manageable size for viewings compared with Devon or Cornwall further west, and prices sit a little below neighbouring Hampshire, making it a sensible county to widen into if the New Forest area feels expensive.