I am possitive that your grandfather many times removed is not a Cherokee indian. The Sneed/Snead/Sneade/Sneyd name came from Staffordshire, England and has been traced back to 1050 AD. There is also a Family Crest that consist of a shield and two lions facing each otherwith their claws raised.
In West Virginia the predominate Indians were the Moneton, Shawnee, Eastern Woodland and the largest tribe was the Appalachian Tribe.
With the Surname Snead, He would not have been full blooded Cherokee. At the most he may have been half Indian. The Virginia Church in or around Shrewsbury, WV has a grave yard with a Henry Snead who passed away in the late 1800s ( my ggg grandfather) and several more on the hill. These are great resources for for information.
There is a lot of information about the Snead/Sneed family in Albamarle County, Virginia that may beof some interest to you.
I do know this for a fact: My great grandfather was John Allen Snead who was born in 1874and died in 1974 had such blue eyes that there was no possible way Indian blood flowed through his veins.
Good luck in your search for your identity of your family but don't let the current culture give you any disillusions.