Jean M. Hoffman, CG
The father of Mary, second wife of Moses Nichols of New Windsor, Orange County, New York, could be the David Wright of whom I've written.  Looking for evidence of a connection requires examining more of the records from David Wright and his associates.
Two accounts emerge from descendants of different alleged sons.
- Three related DAR applications claim patriot ancestor David Wright of New Windsor who served in the Second Ulster Regiment. Their descent is through a son Benjamin who allegedly died in 1820 and his wife Jane Gregg. The applications state that David died in 1833 in New Windsor. Benjamin was born about 1774, his mother wife #2, Margaret Woodhull. The record copy of the last application refers to family records, but there appear to be no supporting documents filed with it. 
- Descendants of a son John wrote up research results. They are reflected in a 1987 compilation.  The compiler has provided me with a copy of the 14-page typescript Francis Wright and Maude E. (White) Cleghorn produced. They indicate David Wright of New Windsor was from Hempstead, then Queens County, on Long Island. Census records for David in New Windsor in 1800, 1810, and 1830 were not located somehow, just 1790 and 1820. One conclusion was that David moved after 1823 to live with a son, Nathaniel, in Warwick, another town in Orange County. Conversely, on another page is the suggestion that Nathaniel returned to New Windsor to care for his elderly parent. The latter could be correct, but David Wright, age 80 through 89, has a household of himself and a female not quite as old, age sixty through sixty-nine, and no others in 1830. 
An important document referenced in #2 above is a deed from David Wright, carpenter, and his wife Mary of New Windsor in 1783 selling land in Hempstead to Nathaniel and Samuel Wright of Hempstead. One of the witnesses was a Benjamin Wright. The deed was recorded in 1799. I need to find a copy of this deed! The 1785 will of this Nathaniel Wright refers to a brother David Wright. 
Missing in any of this research or my own had been records of purchases of land in New Windsor or distribution of it following David's death. Because New Windsor was transferred to Orange County from Ulster County in 1798, I checked deeds in Ulster County. Two pertinent deeds were recorded there.
In 1774 Benjamin Wright, a house carpenter of Hempstead, Long Island, purchased two parcels in New Windsor from Reuben Weed and his wife Martha. The deed was recorded at the request of Mr. Benjamin Wright in 1787. 
In 1791, seventeen years later, David Wright and his wife Mary sold to John Wright, all of New Windsor, one of the parcels and part of the other purchased in 1774 by Benjamin Wright. The deed provides no insight on David's acquisition of title to the land.  A common reason for an unrecorded transfer is inheritance. Could David be a son of Benjamin? If so, what relation is John Wright?
Records in Hempstead, especially the eight-volume published town records, show several generations of Wrights in that location.  More research here might be worthwhile and David Wright's 1783 deed is needed. I have created a timeline for all Wright surname events I've found connected to New Windsor. One for Hempstead may be needed as well.
Still, this sheds no new light on the disposition of David's land after his death. Orange County deed indexes need to be followed further into the 1800s in hopes of finding a link to his heirs.
- Jean M. Hoffman, Wright blog posts on Bluegrass and Buckeye Roots: “Finding Mr. Wright?” (http://bluegrassandbuckeyeroots.blogspot.com/2011/05/finding-mr-wright.html : 20 May 2011); “Mystery Monday: Still No Mr. Wright (http://bluegrassandbuckeyeroots.blogspot.com/2011/06/mystery-monday-still-no-mr-wright.html : 20 June 2011); and “David Wright may be Mary's 'Mr. Wright'” (http://bluegrassandbuckeyeroots.blogspot.com/2012/07/david-wright-may-be-marys-mr-right.html : 30 July 2012).
- Membership application, Mirbell Shirey Pairan, National no. 226286, on David Wright (1745-1883, New York), approved 1926 or after; National Society Daughters of the American Revolution, Office of the Registrar General, Washington, DC; digital images, Daughters of the American Revolution (http://www.dar.org/national-society/genealogy : purchased 28 August 2012).
- Douglas Wright Cruger, A Genealogical Dictionary of Wright Families in the Lower Hudson Valley to 1800 (Bowie, Md: Heritage Press, 1987), 25.
- Francis Wright and Maude E. White Cleghorn, “Wrights of Long Island,” 14-page typescript of now unknown origin, photocopy provided to the author by Douglas W. Cruger, 2015; citing a deed from David Wright and wife Mary to Nathaniel and Samuel Wright (1783, recorded 1799) presumably in Queens County, NY. Regarding U.S. census records, the 1800 and 1810 are cited in my blog posts (see #1 above) although the 1800 is in error as David and John Wright were enumerated in New Windsor but mis-indexed as Newburgh which ends in the top half of their page. Also, 1830 U.S. census, Orange County, New York, New Windsor, p. 103, line 14 for William Wright and line 18 for David Wright; digital images, Ancestry.com (www.ancestry.com : accessed 21 May 2010); citing NARA M19, roll 113; imaged from FHL microfilm 0,017,173.
- Will Record 38: 172-73, Will of Nathaniel Wright (1785); New York County Surrogate's Office, New York, NY, apparently later copy of original Queens County record; digital images, “New York Probate Records, 1629-1971,” FamilySearch (https://familysearch.org : accessed 5 November 2015); imaged from FHL microfilm 866,989.
- Deed Record vol. 9 – II: 509-14, deed Reuben Weed and wife Martha to Benjamin Wright (1774, recorded 1787); Ulster County Clerk's Office, Kingston, NY; digital images, “New York Land Records, 1630-1975,” FamilySearch (https://familysearch.org : accessed 3 November 2015); imaged from FHL microfilm 944,744. After 1798 land in the Town of New Windsor is in Orange County, New York.
- Deed Record vol. 11 – LL: 480-82, deed David Wright and wife Mary to John Wright (1791, recorded 1794); Ulster County Clerk's Office, Kingston, NY; digital images, “New York Land Records, 1630-1975,” FamilySearch (https://familysearch.org : accessed 3 November 2015); imaged from FHL microfilm 944,749.
- Benjamin D. Hicks, editor, Records of the Towns of North and South Hempstead, Long island, New York [1654-1880], Volumes 1-8 (Jamaica, NY, Long Island Farmer Print, 1896-1904). Also digital images at Internet Archive.