You are of course quite right that Horvath in Hungarian means Croat. However it is also a very common surname in Hungary and was my father's surname as well.
However, I have been trying to follow my ancestors trail back on my mother's side, and her maiden surname was Farkas, which is also a common surname in Transylvania, (Erdely pre 1920, when that part of present day Romania was part of Hungary, prior to the Trianon Treaty.)
My parents decided to move to Hungary in 1939 and treated as refuges. I grew up and lived in Budapest untill the 1956 revolution. - Then with 200 000 others, left the Country. Myself migrated to Australia and now at retirement age, decided to do my Family Tree.
The research in Romania is very difficult, therefore grateful to Isabella Szilagyi for her assistance in trakking back to the documents of my GG Grand parents.