To try and identify the Moody M Hale from the question I have looked for other men with the same name.
NOT HIM
So far I have found only one other Moody Hale for who the timeline seems to be:
- born 17 Apr 1820 at Rindge, Cheshire County, New Hampshire, USA
- married Charlotte S Keyes on 6 Jan 1844 at Rindge, Cheshire County, New Hampshire, USA
- born 20 Apr 1824 at Rindge, Cheshire County, New Hampshire, USA
- died 3 Feb 1847 at Jaffrey, Cheshire County, New Hampshire, USA
- in the 1850 Federal Census he is a 30yo Farmer living at Rindge, Cheshire County, New Hampshire, USA with Emerson Hale 67, Jemima F Hale 63, Harris Hale 36, Jemima F Hale 27 and George Phillips 15.
- married Sarah E Wright in 1853 at Fitzwilliam, Cheshire County, New Hampshire, USA
- born 27 Mar 1827 at Enosburg, Franklin County, Vermont, USA
- died 11 Jun 1859 at Rindge, Cheshire County, New Hampshire, USA
- died 28 Apr 1860 at Rindge, Cheshire County, New Hampshire, USA
This Moody Hale seems to be about 20 years too young for the Moody Hale who was living in Albany for the 1855 Census.
NOT HIM
Then there is a Moody Hall who married Mary Estabrook on 6 Jun 1810 at Lebanon, Grafton, New Hampshire, but about him I know little, but he seems to be just a little too young to marry if the Moody M Hale/Hall we are looking for was born around 1797-1801.
THIS APPEARS TO BE HIM
However, I have now found Moody March Hall who seems to be the most likely candidate.
- born 29 Apr 1794 at Cornish, Cheshire, New Hampshire, United States
- married Martha Joslyn Chase on 21 Oct 1816 at Cornish, Sullivan, New Hampshire, USA
- born on 04 Dec 1791 at Cornish, Sullivan, New Hampshire, USA
- died on 07 Dec 1869 in Cornish, New Hampshire, USA
- in the 1820 Federal Census in Cornish, New Hampshire, USA, Moody M Hall heads a household where the oldest Free White Male Person is aged 16 thru 25 and the oldest Free White Female Person is aged 26 thru 44
- in the 1830 Federal Census in Cornish, New Hampshire, USA, Moody M Hall heads a household where the oldest Free White Male Person is aged 30 thru 39 and the oldest Free White Female Person is aged 30 thru 39
- in Q1 1838 Moody March Hall of Cornich (Cornish?), United States received a patent "for a revolving cylinder, applicable to cannon and fire-arms of all kinds" from the French Government. I think this means that he must have visited Europe at least once and could help tie him to the 1845 voyage from London to New York aboard the Prinz Albert.

- in the 1840 Federal Census in Cornish, New Hampshire, USA, Moody M Hall heads a household where the oldest Free White Male Person is aged 40 thru 49 and the oldest Free White Female Person is aged 40 thru 49
- in the 1850 Federal Census he has not been found but wife Martha J Hall 59 and daughters Martha A Hall 30 and Lucy L Hall 20 are living in Cornish, New Hampshire, USA
- he has not been found in any later census - unless that is him in the 1855 New York State Census
- in the 1860 Federal Census he has not been found but wife Martha J Hall is living in Cornish, New Hampshire, USA
- on Ancestry.com there is an intriguing but unsourced record of his death on 22 Jul 1866 at New York, New York, USA. That same unsourced record says that he had four children: Daniel Chase Hall (1818-?), Martha Amanda Hall (1820-1871), Lucy Louisa Hall (1829-1903) and Mary Isabella Hall (1833-1846). Other records have been found for each of these children.