South Yorkshire is built around Sheffield, Doncaster, Rotherham and Barnsley, and much of its equestrian scene reflects that post-industrial geography — reclaimed colliery land and urban fringe fields rather than open moorland, though the Peak District is close on the western edge for those who want it. Doncaster in particular has a long-standing horse culture thanks to its racing history, and there is a solid supply of riding schools and liveries serving a large population.
Because so much of the county is urban or ex-industrial, good grazing is at more of a premium than in rural North Yorkshire, and many ponies are kept on smallholdings or shared yards rather than large fields. That is not a negative for a family — ponies used to a busy yard with lots of comings and goings are often well socialised and unfazed by activity — but do ask about turnout, since restricted grazing is more common here than in the Dales.