Based on additional research and your help, I believe Ruth Carter was Ruth Hendee before her marriage to Phederus Carter (sometimes Cartter). There is some question as to whether Phederus is the father of Dr. Horatio Hendee of Lowville, New York since Horatio used his mother's maiden name and was born (abt 1826) seven years prior to the death of Phederus' first wife (1833) and about nine years before Phederus' marriage to Ruth Hendee (1835). I have been able to find no information on the father of Dr. Horatio Hendee of Lewis County, New York.
For my Hendee research, what I really would like to determine are the identities of the parents of Ruth (Hendee) Carter (or Cartter).
Ruth Hendee b. 1795 Vermont, USA m. Phederus Carter (or Cartter) 1 Jul 1835 West Furin, Lewis County, New York (mother and father[?] of Dr. Horatio S. Hendee and grandmother and grandfather of Dr. Leslie Hendee) d. 20 Sep 1878 Lowville, Lewis County, New York Residence: Harrisburg, Lewis County, New York (1850); Lowville, Lewis County, New York (1878) ["New York, State Census, 1875," index and images, LDS FamilySearch https://familysearch.org/pal:/MM9.1.1/VT8P-SK7), Ella R. Hendee in household of Horatio S Hendee, Lowville, Lewis, New York, United States; "Ancestral File v4.19," database, LDS FamilySearch(http://familysearch.org/pal:/MM9.2.1/MWM8-VM8), entry for Ruth HENDEL[sp].]
Phederus Carter (or Cartter): b. 6 Jun 1787 Westfield, Hampden County, Massachusetts, USA m(1). Sophia MURRAY, m(2). Ruth Hendee 1 Jul 1835 Lewis County, New York