Hi Jim,
I've done a lot of research in Westmorland County, New Brunswick, and Goodwin is a name I've come across quite often there. I checked the "First Families" section of the New Brunswick Genealogy Society (nbgs.ca) and there's the following Goodwin family, that may or may not be related to yours (the references numbers in the Sources are from the New Brunswick Archives):
GOODWIN: Daniel Goodwin Sr. b. 1734 at Plymouth, Devonshire, England or b. 2 Jun 1736 in Newbury, MA, d. c1823, s/o Daniel Goodwin or Gooden and Elizabeth Bishop: m. c1762 Sara Hunt b. 11 Jul 1747 at Ipswich, MA or County Sligo, Ireland, d. c1824, d/o Thomas Hunt and Mary Smith: settled at Point de Bute, Westmorland County:
Children:
1) David Goodwin born on 19 Jul 1763, married at Stewiacke, NS, Elizabeth Woodworth born 2 Nov 1759 d/o Thomas Woodworth and Judith Briggs of Little Compton, RI: Elizabeth m. (1st) on 2 Nov 1777 Patrick Dartt at Halifax, NS and had a son, Job Dartt: settled at Stewiacke, NS:
2) Daniel Goodwin b. 30 Dec 1764, d. 5 Jun 1852, m. at Dorchester, NB, Miss Palmer:
3) Jonathan Goodwin b. 21 Jan 1767, d. 1847, m. c1794 Elizabeth Chappell d/o Eliphalet Chappell and Katherine Somers:
4) Thomas Goodwin b. 7 May 1769, d. unmarried:
5) Mary Goodwin b. 10 Mar 1771, d. 13 Jun 1783:
6) Enoch Goodwin born 10 Jul 1773, died 1863, m. 1797 Mary Chappell d/o Eliphalet Chappell and Katherine Somers:
7) Benjamin Goodwin born 13 Jun 1775 at Point de Bute, died unmarried:
8) George Goodwin b. 3 Jun 1778, m. Ellen Cummings of Stewiacke, NS:
9) William Goodwin b. 7 Oct 1780, m. Leah Fillmore: had twelve children:
10) Spiller Goodwin b. 1 Nov 1785, d. unmarried:
11) John Goodwin born 6 Jan 1786, m. 9 Sep 1821 Mrs. Sarah (Munday) Faulkner:
12) James Goodwin b. 1 Dec 1788, m. Frances Fillmore: settled at Tidnish, NS and had twelve children.
Sources: MC1/Goodwin #1,2,3, 65 pages: file contains a page from an article titled Early settlers of Cumberland Township, Nova Scotia by Louise Walsh Throop which gives Daniel's birth place as Mass. and reports that Daniel and his brother Enoch Goodwin were in the British Army and single in 1761: in file #3 and it is noted that Daniel's brother Enoch married in 1762 Mary Hunt, sister of Daniel's wife Sarah: a genealogy titled The Goodwin family by Janie G.R. Goodwin notes that Daniel was b. in England and went to Massachusetts, and with brothers, Enoch, William and John Goodwin came to NS with First Battalion of Governor Shirley's Regiment early in 1755 and were involved in the French/Indian wars: see MC80/338 I. Allen Jack’s Biographical Review, pages 368-371: see also MC80/1790 Ken Kanner’s Early families revisited, page 118: see MC80/1804 Fred W. Krech Descendants of Daniel Goodwin and Sarah Hunt: Nova Scotia and New Brunswick: see also MC2852 Purdy-Carter genealogical collection, MS2: on microfilm reel F20987: see sheet for Daniel Goodwin.
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This family came to NB too early to be Loyalists - they would more likely have been New England Planters, who settled in NB in the 1760s.
There are also listings for a few of Daniel and Sara's children and their families, but no sign of a Felix. There is a note that the name is often spelled "Gooden" in early records, so you might want to check with that spelling as well.
There are no listings for a Loyalist family named "Goodwin" in New Brunswick.
