The name seems to be either from the Henwood Village in Cornwall, England, which we are not from, or from Hampshire, England, where I have traced our family. The oldest spelling I have seen is Hynwode found in 1572 in Kingsclere, Hampshire, England. I found a James, John, Wyllm , Dunant and Dorathie there.
12/4/09 From Valerie Henwood, researcher: yes this is the early spelling of the name but Kingsclere is in the North of the county of Hampshire, and as yet [30 years of research] I have not found a connection with these Henwoods and ours in the south of the county, unless it goes further back than the parish records, there are more Henwoods of this early date just on the border in the neighbouring county of Berkshire, and I think these early ones crossed back and forth so to speak,
Valerie on Dunant: She tells me that the Christian name is Conant.
I checked in England and it is not even listed there.