Thanks for the enquiry re Horn/Horne name. I can appreciate that you have difficulty in tracing beyond grandparents or great grand parents, sadly we do not ask enough questions while grand[parents are still alive. We are always too busy with our own lives to think about where you came from.
Tyhe name Horn/Horne is certainly one of the oldest surnames in Europe and is to be found in Norway, Germany, Sweden, Denmark, Holland, Belgium and in Italy and France Cornu, the latin name.
Unless your ancestors of the 4th generation back were recorded for a particular achievment or even crime it is a hard task to progress further, but one is ever hopeful. Have you contacted all known relatives ie cousins etc tosee if they have information beyond pours? Most Horns of the early settlers were in Virginia such men like Richard Horn recorded as over the River in february 1623 or John Horne who was transported to Virginia aboard the ship called the "Transport from London 4th July 1635. Sadly it is extremely difficult to find and prove an unbroken pedigree,lucky are the few in the USA who had ancestors of note and can say that their ancestor William was born in London or Yorkshire and was married to Mary Thompson.
However my book is concentrated on English Horn/Hornes from the early centuries in chronological order and contains a few pedigrees.Also my companion booklet contains over 300 extracts from official documents of the deeds or misdeeds of the Hornes and gives locations, occupations and many other useful avenues of information to help the researcher.
I have bought up the last of the printing and now sell the book direct from my home at a considerably reduced price. If you are interested to purchase a book and/or Companion please reply to my E MAIL address. Best wishes, Geoffrey