Anthony Snow parentage: Volume VI, 2nd Edition of the "Mayflower Families 1-5 generations does not list Anthony Snow as a child of Constance Hopkins Snow and Nicholas Snow. They married in 1627; Anthony is listed as being born about 1615 in England. Their lst child is listed as Mark born 9 May 1628. Anthony's only listed Mayflower connection is thru his wife Abigail Warren, where his name does appear, but no parentage. Anthony and Nicholas might be brothers, but have, as yet, found no definitive info.
Sources:
Robert Charles Anderson, The Great Migration Directory: Immigrants to New England, 1620–1640
A Concise Compendium (Jun 2015) p 313
He cites:
The Mayflower descendant: a quarterly magazine of Pilgrim genealogy and history Vol 13 p 85 (citation for marriage)
Records of the Colony of New Plymouth in New England , Nathaniel B. Shurtleff and David Pulsifer, eds., 12 volumes in 10 (Boston 1855 – 1861) 1:83
The Genealogical Advertiser, v. 1-4 (Cambridge, 1898-1901; rpt. Baltimore, GPC, 1974) 3:90
L. Effingham deForest and Anne Lawrence deForest, Moore and Allied Families: The Ancestry of William Henry Moore (New York 1938) p 470-76
Mayflower Families (the "silver" books) 8: 7-8
For Nicholas Snow see:
Robert Charles Anderson, The Great Migration Directory: Immigrants to New England, 1620–1640
A Concise Compendium (Jun 2015) p 313
Robert Charles Anderson, The Great Migration Begins: Immigrants to New England, 1620-1633 , 3 volumes (Boston 1995) 1701-4; PM 428-32
The Mayflower descendant: a quarterly magazine of Pilgrim genealogy and history 62:39-41