Randolph Snead and his wife Dicey Rousey are my ancestors. I haven't seen any proof that Cary was their son but other's believe so. Certainly the Randolph/Cary/Benjamin Snead connection is alive in the naming pattern but proves little.
There is a widow John Snead m. in Amherst (to Hannah Lane)1793, Elisha Snead, surety
Randolph and Haney Snead m. their spouses on the same day in Amherst Jan 6 1794. Haney's father was listed as John. I deduce from this Randolph and Haney (who m. Wm. Smith) were most likely related, possibly brother and sister which would make John Snead their father. I've haven't researched William Snead. I've been to the Amherst and Nelson couthouses and found nothing more on the family. There are a couple of ended cases for Sneads in Nelson County which I havne't had time to get to yet. I doubt they hold much new information.
Nova Lemons has looked for anything Randolph (probably the on-line genealogy you refer to) but hasn't turned up any property, wills etc.
Albermarle county would be another good place to search. I hope this helps. Contact me via my e-mail if you'd like. Shirley