I know there were Arnolds in Dayton Ohio as far back as 1810. There was a James Oliver Arnold who died in early 1900's in Dayton. I checked Ancestry and there were quite a few in 1870 census. Where did you find the picture? Can you get an idea of the age. I am guessing 1880-1890.
Marilyn
I just added this photo of my grandfather, Ralph H. Oliver 1885-1942. He was an only child of Thomas Oliver (1854-1941) and Mary Francis Harter. Thomas was one of 9 children of Benjamin F. Oliver 1817-1892 and Sebethany Westlake. I have not been able to confirm where Benjamin was born but some records said Augusta County VA. He died in Dayton Montgomery County Ohio. I hope Ancient Faces will notify me of any emails!