On each occasion, the horse is ridden by her father.

It's possible that even for him (except, presumably, when he's transporting things to market) the usual mode of travel is by foot. (See O15 , O17 , O20 , N12 .)

Mr. Beamish has a horse—which brings him to Colin Grove on Sept.14. And when the Stuarts visit Colin Grove on Nov. 27, they evidently come in a chaise or some kind of horse-drawn vehicle.