A “blue norther” (or simply “norther” or “Texas Norther”) is a strong northerly wind that’s also combined with a decrease in temperature. The term dates from the early 1800s.
 
The Dictionary of American Regional English states that “blue” is an intensifier meaning “extreme,” but it could be simply that “blue” means “blew.”
 
 
Handbook of Texas Online
BLUE NORTHER. The term blue norther denotes a weather phenomenon common to large areas of the world’s temperate zones–a rapidly moving autumnal cold front that causes temperatures to drop quickly and that often brings with it precipitation followed by a period of blue skies and cold weather. What is peculiar to Texas is the term itself. The derivation of blue norther is unclear; at least three folk attributions exist. The term refers, some say, to a norther that sweeps “out of the Panhandle under a blue-black sky”–that is, to a cold front named for the appearance of its leading edge. Another account states that the term refers to the appearance of the sky after the front has blown through, as the mid-nineteenth-century variant “blew-tailed norther” illustrates. Yet another derives the term from the fact that one supposedly turns blue from the cold brought by the front. Variants include blue whistler, used by J. Frank Dobie, and, in Oklahoma, blue darter and blue blizzard. Though the latter two phrases are found out-of-state, blue norther itself is a pure Texasism. The dramatic effects of the blue norther have been noted and exaggerated since Spanish times in Texas. But that the blue norther is unique to Texas is folklore.

BIBLIOGRAPHY: Dictionary of American Regional English, Vol. 1 (Cambridge, Massachusetts: Harvard University Press, 1985). 

(Dictionary of American Regional English)
norther n chiefly TX
A usu strong northerly wind that often brings a sudden decrease in temperature.
 
1820 in 1858 Dewees Letters TX 17, A heavy storm of rain and sleet, together with a furious “norther” overtook us.
1834 (1928) Underwood Jrl. 32.129 TX, We were much in fear that a norther would spring up, in which case all of us must have been consigned to a watery grave.
1835 in 1952 Green Samuel Maverick 36y TX, Yesterday at about same hour a norther blew up, bringing the thermometer down 20 degrees, fro 75 degrees to 55 degrees.
1845 in 1868 McCall Letters Frontiers 431 esTX, If the Norther is accompanied by rain in the form of sleet, it is of course the more severe. Not a fortnight since, we had one of these Wet Northers, as they are called.

(Dictionary of American Regional English)
blue norther n. Also infreq. blue Texas norther, blue-tailed norther [blue adj. 3 + norther a northerly wind] TX See also norther CF blue blizzard, blue darter, blue whistler.
A cold wind from the north that brings rapidly falling temperatures.
 
c1856 in 1947 AN&Q 7:144 TX, On page 187 of the second volume of Ordeal of the Union, Allan Nevins, treating of the cattle country of Texas, refers to a record (from the University of Texas Archives) written by an early cattle driver. The driver speaks of a “blew-tailed norther,” which he encountered on a cattle driver sometime around 1856. Such winds, he says, were “very common in Texas 40 or 60 years ago.”
1873 Morrell Flowers & Fruits 234 TX, A blue Texas norther whistled around my ears.
     
7 January 1832, Cincinnati Mirror and Western Gazette, pg. 57:
Those acquainted with the Gulf of Mexico and its winds, will recognize, among the latter, one that is aptly termed the Norther. It is one of the heaviest and most frequent gales that blow in any sea; and, on this account, together with the exposed and dangerous situation of the southern coast of the Gulf, is an object of peculiar dread to the navigators of that sea. It rises frequently with such suddenness; that the most alert have hardly time to prepare to meet it, and it continued, with slight intermissions, during the whole winter.
 
8 February 1836, Army and Navy Chronicle, pg. 136:
The reputed severity of the Northers, which blow in the Gulf at this season, had made us, for the whole passage, greatly dread our cruise to Texas. On the slightest indications of one, every thing was put in readiness, so that we suffered comparatively nothing from their visitations. The most violent we experienced blew for about sixty hours; this is longer than they ever continued, we were told by those who had felt them before. The thermometer ranged between 73 degrees and 57 degrees Fahrenheit, during the while, and the temperature of the climate off the coast did not much vary from 62 degrees.
 
28 May 1842, The New World, “Letters from Mexico” by Brantz Mayer, pg. 339:
DURING the last two days of our delay at Vera Cruz it blew a Norther. The wind was furious, and made it impossible for ships to enter the port.
 
21 August 1857, Chicago Daily Tribune, American Association for the Advancement of Science Eleventh Annual Meeting, pg. 2:
THE TEXAS “NORTHER.”
Mr. Forshay then made some remarks upon the climate of Texas, and upon the nature and causes of the wind called the “Norther,” which prevails in that State. After giving some particulars respecting the winds and climate of Texas, the gentleman stated, as the result of his observations, that from the dryness of the soil and climate, but a small tract of the immense region west of the Colorado River, (forming nearly half the territory of the United States) could be cultivated without the aid of artificial irrigation. He then went on to describe the Texas Norther. This wind, which always come from the north, generally occurred during winter from November to April. It was always preceded by very hot weather; but the moment it began to blow the thermometer fell with great rapidity. In one instance he had known it to fall 20 degrees in as many seconds. At the place where it commenced, it blew with great violence, or, as the inhabitants describe it, struck “but-end foremost.”
 
Although at the commencement of the storm there was frequently a shower of rain, produced great dryness in the atmosphere causing papers to end up and furniture to crack, while the earth appeared to have its moisture “drunk up from it.” This wind was the great bugbear of Texas, and was dreaded by every one and in speaking of the weather people did not say it is going to rain to-day, but “there is going to be a Norther.” Nothing certain was known as to the cause of this wind, but this theory was that it was caused by a sudden downward current of air from the cold strata of wind from the top of the Cordilleras. He had no barometric observations with regard to it, but the sudden changes in the temperature and atmosphere which it caused were quite apparent. These storms generally blew once in seven or eight days, their duration being from 12 hours to occasionally three days. It was a remarkable fact of eleven of these storms of which he had kept a record, ten fell upon Saturday.
 
16 March 1869, San Antonio Express, pg. 3:
THE WEATHER.—Sunday night about 12 o’clock, a rain set in, and closed with a regular blue norther, blowing a perfect hurricane.
 
21 January 1870, Fort Wayne (IN) Daily Gazette, pg. 4:
SNOW is three inches deep in Texas, and blue northers make people anxious to remain indoors.
 
28 May 1874, Chicago Daily Tribune, pg. 3:
A Texas Norther.