Either our subject was re-buried or the name of the cemetery changed or there's an error in the entry at Find-A-Grave.  Note that I cannot find a Brown Hill Cemetery on a search at Google.

Either our subject was re-buried or there's an error in the entry at Find-A-Grave because the McDowell Cemetery still exists.

1.  Marriage Record:

2.  1850 U.S. Census Every-Name-Index/Images (online at Ancestry.com):  Leonard HARTER (æ 25, b. NY) is living in Wayland, Steuben Co., NY, with his parents (p. 164B/328), Adam HARTER (æ 52?, b. NY) and Adelia (æ 52, NY), plus siblings.  Sarah RAZEY (æ 12, b. NY) is living in the Town of Almond, Allegany Co., NY, with her parents (q.v.).

3.  1860 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #
 

.  Find-a-Grave: Entries (online at findagrave.com):

Except for the tombstone images and occasional mention of a death certificate, this database consists of undocumented patron submissions, so caveat emptor.
Name:	Leonard Harter	Sarah Jane Razey Harter	David Henry Harter	Ertram Harter	Dillie Harter	Harriet Harter	Mae F Harter	Dee Harter
Birth:	25 Sep 1824 Howard	Jan. 11, 1838, Allegany, Cattaraugus Co., NY	Jun 24, 1857	29 Sep 1861, Cohocton, Steuben Co., NY	20 Aug 1863	09 May 1868	Mar 12, 1870, Cohocton, Steuben Co., NY	06 Aug 1874, Cohocton, Steuben Co., NY
Death:	Mar. 2, 1908, at home	Dec. 5, 1892, Cohocton, Steuben Co., NY	May 17, 1949	16 Apr 1943	12 Dec 1931	10 Nov 1927	May 8, 1948, New York, USA	07 May 1949, Wayland, Steuben Co., NY
Burial:	Maple View Cemetery Cohocton, Steuben Co., NY	Maple View Cemetery Cohocton, Steuben Co., NY	Maple View Cemetery Cohocton, Steuben Co., NY				Maple View Cemetery Cohocton, Steuben Co., NY
Inscription:	Co G 169th NY Vol
Father:	Adam Harter	Robert Razey (1777-1874)	Leonard Harter
Mother:	Matilda	Sally Bigelow Razey (1793-1880)	Sarah Jane Razey
Spouse:	Sarah Jane Razey Harter	Leonard Harter		Nellie Teed	Harvey G. Teed	Henry J. Bill		Bertha J. Whitman
Obituary:	(unknown paper; boldface added) Leonard Harter, Aged 83 Years, Died at His Home Sunday Night. Leonard Harter... died at his home here Sunday night after a weeks' illness of lung trouble...  Leonard Harter was the son of Adam and Matilda Harter and was born in the town of Howard, September 25, 1824. He was one of a family of twelve children... His wife died December 5th, 1883. Mr. Harter was a veteran of the civil war, having enlisted Sept. 1st, 1864 in Co. G, 189th Regiment N.Y. Vol. Infantry, and served until the close of the war, being discharged on the 30th day of May, 1865. He was a member of E.R. Harris Post, G.A.R. Cohocton...  He is survived by one brother, who resides in South Dakota; a brother who resides in Brown Hill, in the town of Cohocton and sister, Mrs. Willis Adams of Hemlock, and three sons and three daughters, David, of Buffalo; Ertam and Dee, of this village; Mrs. Dilla Teed, of Springwater; Mrs. Henry Bills, of Cohocton and Miss May, of this village with whom he resided, besides several grand-children. Funeral services were held at the home yesterday morning at 10:30 and interment was in the Brown Hill cemetery. (Courtesy Leola J. Moore)	(unknown paper; boldface added) Mrs. Sarah J. Harter, wife of Leonard D. Harter, died at her home on Brown Hill, Monday evening, Dec. 5th, 1892, at 10 o'clock... Mrs. Harter was the daughter of Mr. and Mrs. Robert Razy. She was born in Allegany county, N.Y. January 11, 18__. Since her marriage, 30 years ago, she has resided on the farm where she died... She leaves to mourn their loss a husband, three sons, David, Ertram and Dee, and three daughters, Mrs. Harvey Teed and Mrs. Henry Bill, of Wayland, and Miss May who resides at home as does also her brother Dee... The funeral services were held in the Presbyterian church in this village this afternoon at one o'clock, the Rev. John Waugh officiating. The burial was in McDowell cemetery. (Courtesy Leola J. Moore)
Contributor:	Robin Cleland	Robin Cleland	Robin Cleland				Robin Cleland
Memorial #:	15444877	15444876	15444874				15444878

Is "this village" Brown Hill?

.  New York, Town Clerks' Registers of Men Who Served in the Civil War, ca 1861-1865.  New York State Archives, Albany, NY (online at Ancestry.com):

Names:	Harter Leonard
Residence:	Cohocton Steuben Co NY
Time and Place of Birth:	Sept 25 1825 Howard NY
Rank | Regt | Co:	Private | 189 Inft | G
When Enlisted:	Aug 29 1864
When Mustered and Rank:	Sept 7 1864 Private
Enlisted for (Month Year):	1 Y
Place of Enlistment:	Cohocton
Race:	W
Bounty Paid by Town:
Bounty Paid by County if disbarred by Supervisor:	$800
Relief granted to family by Town:
Single / Married:	M
Names of Parents:	Adam Adelia Helmer
Previous Occupation:	Farmer
Promotions, Resignations, Discharges, Deaths, &c, with Dates, Causes, &c.:	In the battles in front of Petersburgh and Richmond Post Office [unreadable]
If deceased, state whether by Disease, Accident of on the Field of Battle:
Give Place of Burial:
If not deceased and out o fService give present Post Office Address:	Cohocton Steuben Co New York
Source:	Collection Number (N-Ar) 13774; Box Number 57; Roll Number 31

.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).