From Wikipedia:

The term "nor’easter" comes to American English by way of British
English and the points of the compass and wind or sailing direction.
According to the Oxford English Dictionary (OED), the first
recorded use in the English language of the term "nore" ("north") in
association with the points of the compass and wind direction is by
Dekker in 1612 ("How blowes the winde Syr?" "Wynde! is
Nore-Nore-West."), with similar uses occurring in 1688 (". . . Nore and
Nore-West . . .") and in 1718 (". . . Nore-west or Nore-nore-west.").
These recorded uses are predated by use of the term "noreast," first
recorded as used by Davis in 1594 ("Noreast by North raiseth a degree
in sayling 24 leagues."). Thus, the manner of pronouncing from memory
the 32 points of the compass, known in maritime training as "boxing the
compass," is described by Ansted (A Dictionary of Sea Terms,
Brown Son & Ferguson, Glasgow, 1933) with pronunciations "Nor’east
(or west)," "Nor’ Nor’-east (or west)," "Nor’east b’ east (or west),"
and so forth. According to the OED, the first recorded use of the term
"nor’easter" occurs in 1836 in a translation of Aristophanes. The term
"nor’easter" naturally developed from the historical spellings and
pronunciations of the compass points and the direction of wind or
sailing.

As noted in a January 2006 editorial by William Sisson, editor of Soundings
magazine, use of "nor’easter" to describe the storm system is common
along the U.S. East Coast. Yet it has been asserted by some that
"nor’easter" as a contraction for "northeaster" has no basis in
regional New England dialect and is a "fake" word, which is a parochial
view that neglects the little-known etymology and the historical
maritime usage described above.

Common coastal New England pronunciation (both seafaring and not)
for "nor’easter" is “naw-EE-stuh” (like "LOB-stah" for "lobster"). Off
the coast (Vermont), the pronunciation is closer to "noar-eastuh".
According to a handful of 20th-century Maine-based authors, Downeast
mariners historically pronounced the compass point "north northeast" as
"no’nuth-east," and so on. For decades, Edgar Comee, of Brunswick, Maine,
waged a determined battle against use of the term "nor’easter" by the
press, which usage he considered “a pretentious and altogether
lamentable affectation” and “the odious, even loathsome, practice of
landlubbers who would be seen as salty as the sea itself”. His efforts,
which included mailing hundreds of postcards, were profiled, just
before his death at the age of 88, in The New Yorker.^[1]

Despite the efforts of Mr. Comee and others, use of the term continues by the press. According to Boston Globe writer Jan Freeman,
“from 1975 to 1980, journalists used the nor’easter spelling only once
in five mentions of such storms; in the past year (2003), more than 80
percent of northeasters were spelled nor’easter”.^[2]

University of Pennsylvania linguistics professor Mark Liberman has pointed out that while the OED
cites examples dating back to 1837, they represent the contributions of
a handful of non-New England poets and writers. Liberman posits that
"nor’easter" may have originally been a literary affectation, akin to
"e’en" for "even" and "th’only" for "the only", which is an indication
in spelling that two syllables count for only one position in metered
verse, with no implications for actual pronunciation.^[3]