Sarah and her friends start a riding club during the summer holidays so they can improve their riding. The “Surprise” element comes in as each President is supposed to provide a surprise for the members when they finish their time as President.
Most of Elinore Havers' books were published in the Crown Pony Library series. The Surprise Riding Club was published by Collins, and made an appearance in the Collins Pony Library. I wonder if the appearance of her books in pony libraries is the key to understanding her appeal: she writes books which tick all the boxes required by the pony lover, and is utterly reliable in doing so.