I looked through the NARA records this evening. He also served as brigade blackmith, so his occupation on the 1860 census might be something other than a farmer. There's also a man named William A. Hall in the same company. You might check to see if this man appears in a nearby household.

I see no reference for him in Company "H", which happened to be a Jefferson County company.

You might also consider checking the 1860 Alabama census for this man, since his age (about 36) would indicate a head of household. If there's another Hall by this name living in Walker County who's about this age, it's unlikely that he's the same person. Unlikely, not imposible.