C E Heanley (Charlotte Elizabeth Heanley, 1864–1946) wrote Peter, a story of animals and children (and of course a horse) set in a country house in Suffolk. The book is easy to find (a little less so with its dustwrapper) and has charming illustrations by Frank Hart. Charlotte Elizabeth Heanley also wrote 'tis Known in Appin, The Toll of the Marshes, The Granite Hills and a booklet of short stories, In Cornwall by the Sea.
Her sister’s diaries (Dr Katharine Heanley) exist in extract form on the internet, and this reference has a sketch of Honey Hill, in Cambridgeshire, which is where Charlotte was born.
Finding the book
Reasonably easy to find, and generally reasonably priced.
John Starr, personal correspondence and an extract from the diaries of Dr Katharine Heanley