Henry is living with his brother in 1850 census
1850 census at Hoosick Rens., Co., NY., page 367
Joseph Barnhart age 59 b. NY
Hannah age 48 b. NY
Belinds age 12 b. NY
Mary E. age 10 b. NY
next door
David Barnhart age 83 b. abt 1767 NY
Lucretia age 83 b. NH
Henry age 68 b. abt. 1782 NY
Stephen A. age 40 b. NY

He is confused with
1850 Sept. 4 Census - Persia, Cattaraugus Co., NY. page 349
BARNHART Henry D. age 50 b. NY -- Wagonmaker
Lydia age 38 b. NY
William C. age 21 b. NY -- carpenter
Roxana M. age 19 b. NY
Catherine A. age 17 b. NY
Jacob D. age 13 b. NY
Benjamin F. age 11 b. NY
Hiram H. age 8 b. NY
Albert age 4 b. NY
FULLER David age 21 b. NY carpenter

History of Royalton Vermont PART 2 by Evelyn Lovejoy pub 1911
page 811
Lucretia Handy m. David Barnhart Lucretia d. March 1854 and David d. Feb 1852.

page 812 lists their children
1. Joseph b. 1792 Sept 21 d. 1870 Aug 12 m. Hannah Hodges
2. Michael , of whom nothing is known--familysearch.org Michael D. Barnhart 1794-1870 married Charity Blass.
3. Henry , d. 1865 April 8, Sandgate, aged abt. 70
4. Maria b 1811 Oct 1 or June 1812 d. 1884 Feb 6 m. John B. Covey
5. Lucretia d. unmarried -- insane
1850 Aug 16 Hoosick, Rensselaer Co., NY census
John Martin age 35 b. Ireland
Elizabeth Martin age 5 b. NY
Betsey Martin age 68 b. Ireland
Lucretia Barnhart age 40 b. NY - insane
6. Lucinda m. R D Ferris
7. Juliette m. William Holcomb-- Juliette is findagrave mem ID
71637437
8. Henrietta m. Dr. Chadwick
9. Gideon b. 1792 d. 1889 Aug 6 m. Martha Holmes--they were living in Collins, Erie Co., NY 1850-1875. Then 1880 June 5 Sandgate, Bennington VT census, Gideon (married) age 85 lives with his sister Maria Covey (widow) in the household of her daughter and her husband E f Hoyt.
10. Roxana b. 1819 May 20 d. 1877 May 12 m. William Stoney
11. Stephen m. Esther Fort