I am a "Winningham" researcher, and also found this site when attempting to explore deviations of that surname.One published account for a Theodore Winningham indicates his family was related to a "Wintringham" in England who was a personal physician to King George III.I am unable to prove this connection.
In my searches, I have also came across another similar spelling, "Winteringham."This was a marriage record, October 7, 1893 for an Ira Winteringham, in Deleware County, Indiana.It indicates that Ira was the son of George Winteringham and Bell (German) Winteringham.And, in the same county during this time are people with the name of Winningham?
If you have any information that can shed light on a possible connection of these people, I would appreciate hearing from you.
I also spent a few hours looking at the census records for Wintringhams that were in New York early back about 1800.These are probably the people you are speaking of.I don't know how much information you may have on these people, but I would be happy to share the little information that I have if you do not already have.