Yes, it's certainly a mystery as to why they never seem to be around when the Census takers showed up in 1860 and 1870. I found William, Elizabeth, Andrew and Winnie in the 1880 Census in Magazine, Yell County. I wonder who the folks are in Woodruff? In the 1870 Census for Yell County (Dardanelle), there is a house listed (with no information) between Hardin Walker and Joel Walker. One of the Walker's (William Albany Walker) married Malissa Jane Davis (daughter of William Davis). My cousin and I speculate that William and Elizabeth Davis lived in that house for which there is no information. We find him on Voter registration rolls, he purchased land in 1860 in Yell County and later homesteaded other land there. He's just not there when the census is taken which is very frustrating!
So, do you think the man in the 4th AR Cavalry is a different William Davis?