North Yorkshire is a serious pony county. The Dales and the Moors both breed native ponies, there is a long-standing hunting and Pony Club tradition, and the showing scene is strong. For a family, that means genuine choice between hardy moorland-bred natives and produced ponies with a competition record.
It is also a big county with real distances between areas — a pony near Skipton and one near Whitby are the best part of a hundred miles apart. Ponies from the moors and dales are typically good on their feet and unbothered by weather and hills, which makes them excellent all-rounders for families who hack out. If your child will be riding mainly in an arena, that toughness is still useful but ask about schooling specifically, since a pony can be brilliant across country and green in a school.