The following biographical information has been provided by Lee Viverette, reference librarian at Virginia Museum of Fine Arts, Richmond, Virginia.
He exhibited three portrait paintings at the National Academy of Design in 1858. Address in 1858 was 137 Montague Place, Brooklyn.
Source: National Academy of Design Exhibition Record 1826-1860. N.Y., NYHS, 1943.
From Artists in Virginia before 1900, An Annotated Checklist, by R. Lewis Wright, University of Virginia, 1983.
Entry reads "flourished 1818-58. Portrait, miniature, and landscape painter. He worked in Richmond [VA] in 1818; in 1829-56 he was in Boston; in 1857-58 he was in Brooklyn.
This source also references a biographical entry in the New York Historical Society's Dictionary of Artists in America, 1564-1860. by George C. Croce and David Wallace. New Haven: Yale University Press, 1957.
A portrait of Edward Cunningham (1771-1836) by Hudson is depicted in Richmond Portraits, In an Exhibition of Makers of Richmond, 1737-1860. Richmond: Valentine Museum, 1949. (# 40. p. 54.) Reproduction is in black and white but described as " Background greenish olive; red chair; reddish blonde hair, blue eyes, rosy complexion."
Described as miniature on ivory. 3 x 2 1/2 inches. Painted 1818. Signed, upper right: W. Hudson 1818. Lent by Mrs. Richard E. Cunningham. A biographical entry for Hudson is on p.221 (same info)