If you check out the 1920 census for Arab, Marshall County Alabama, I believe that you may find that Montgomery Skidmore was the father of your great-grandfather Houston Skidmore. Montgomery Skidmore was, according to this census was born about 1871 in Alabama.
Also if you check the 1880 Census for WARRENTON P O, Marshall County, Alabama you may conclude that Nathaniel Skidmore was the father of Montgomery Skidmore. Nathanial Skidmore, according to this census was born about 1843 in Alabama.
I can be contacted at firstname.lastname@example.org if you net images of these census records.
I am not to my knowledge related to the Skidmores but my 4th great-grandfather, Anthony Houston participated in the Battle of Fort Pleasant (in present day West Virginia) on 10 October1774 in the same company with an Andrew Skidmore, son ofJoseph Skidmore.