States: Connecticut: Fairfield
On the free side of Ancestry.com I found on the ancestry world tree a lot about this family. Do a search on Eli Winton. The first one that comes up (born 1814) is the one you want. By navigating around you'll find that Eli was Harriet's father, but her mother Harriet Hawley, who died in 1855, so the wife on the 1880 census was not Harriet's mother, but step mother. You can also find the exact date of Harriet's birth (16 Dec 1830) and the date of her marriage to Edmund H. Smith (29 April 1979) It also has Edmund's birth date as 14 April 1851. Given their marriage date, it looks like they were only married for the 9 months it took for Walter to be born. I have no idea as to the accuracy of the information on this tree (It's a Hawley Family Tree) but you might contact the submitter (Raymond Hawley) and inquire as to the documentation of what's presented there, or lacking that you can use the info as a starting point and seek the documentation from original records. I don't know if Easton's vital records are online, but certainly the Barbour Collection should have something at least up to the 1850 cutoff for that collection. That collection is available at my local genealogy library, so I may be able to help out.