Hi,
This John Snow could be from my Snow line, but I have many John Snows in my file. None that have Mary Thurston as a wife. This John may be from the William Snow line.
William Snow who in 1635, at the age of 11, had come from England with his master, Richard Derby, and landed in Plymouth. In 1638 he was assigned to another master, Edward Doleio (Doten?). After his seven years' apprenticship he lived for a while in Duxbury and then became one of the first settlers in West Bridgewater. He married "Rebeckak" Brown, daughter of Peter Brown who came on the "Mayflower". (8 Children).
William's decendants came to Providence and there were several generations of pastors of high regard. This may be your line.
Hope that was of some help.