The anonymous author of "The Strange Things Which Happened at Our Christmas Party," in the Christmas 1865 number of London Society (December 1865) contrasts the portent of "a white Christmas" with that of a green Christmas, according to an "old saying":
Whether that old saying be true or not that 'a green Christmas makes a fat churchyard,' it is certainly true that a white Christmas makes a warm fire-side ; and such of us as had learnt the meaning of rheumatism, felt sympathetic aching of the joints whenever any poor old soul trudged past along the trackless road, and wondered if they had a warm chimney corner at the end of his journey.
The "old saying" cited in this story appears in slightly different form (with an interesting discussion) in John Ray, A Collection of English Proverbs (1670):
A green winter makes a fat Church-yard.
This Proverb was sufficiently confuted Anno 1167, in which the winter was very mild ; and yet no mortality or Epidemical disease ensued the Summer or Autumn following. We have entertained an opinion, that frosty weather is the most healthful, and the hardest winters the best. But I can see no reason for it, for in the hottest countries of the world, as Brasill, &c. Men are longest lived, where they know not what frost or snow means, the ordinary age of man being an hundred and ten years : and here in England we found by experience, that the last great plague succeeded one of the sharpest frosty winters that hath lately happened.
Nevertheless, the proverb persisted at least another two hundred years, with only slight alteration (winter giving way to Christmas).
A Google Books search finds instances of "[a] white Christmas" from as early as 1834, although the earliest instance uses "white Christmas" as a modifier for the noun night. From Henry Chorley, "Night in the Streets—Snow," in Sketches of a Sea-Port Town, volume 2 (1834/1836):
How delightful is such a still white Christmas night as this, supposing the snow be all fallen, and the sky bright with its countless stars! There were such things as carols once ; and it was a pleasant thing to watch the bands of little children creeping from door to door, with their ancient ditties, and their voices innocent and tuneless.
The seaport town in question is Liverpool.
From Berthold Auerbach, "Ivo," in Village Tales from the Black Forest, translated by Meta Taylor (1847):
A white Christmas brings a green Easter,—the saying came true this year. The next day was Easter Sunday: all appeared unusually bright and green.
The proverb in this case appears to be German.
From Colburn Mayne, Madeline Clare; or, The Important Secret, volume 3 (1856):
"Dear me, I did not know it was snowing; and your coat is all white; what severe weather!"
"It is good weather, said the farmer, taking off his coat, and rubbing his hands; "a green Christmas makes a full churchyard. I am glad when it is a white Christmas."
"And this is Christmas eve," observed Mrs. Harwood.
And from George Eliot, "The Sad Fortunes of the Rev. Amos Barton," in Littell's Living Age (April 1857):
"Ah," Mrs. Hackit thought to herself, "I dare say we shall have a sharp pinch this winter, and if we do, I shouldn't wonder if it takes the old lady [Mrs. Patten] off. They say a green Yule makes a fat churchyard ; but so does a white Yule too, for that matter. When the stool's rotten enough, no matter who sits on't."
All of these instances are from England. The earliest U.S. match I have come across appears in J. Nelson, "The Weather Guide, and Influence of the Stars, for December, 1849," in the [New York City] Sunday Dispatch (December 2, 1849):
21st to 23d—Severe gales ; snow and frost.
24th to 26th—More temperate ; rfosty air ; a white Christmas.
The spelling "rfosty" is in the original text, but I dare anyone to sing "Jingle Bell Rock" with the line "through the rfosty air" and stay on the beat.
Conclusions
Almost all of the earliest (1834–1860) instances that I found of "[a] white Christmas" in reference to a Christmas marked either by falling snow or recently fallen snow are from England, starting with Henry Chorley's "a still white Christmas night" in 1834. The fact that a well-known English proverb had invoked a "green Christmas"—and before that, a "green winter"— strongly suggests that people in England were at least implicitly drawing a parallel between a green Christmas/winter and a white one, although it is possible that the implied alternative to green was black or brown. In any event, British authors in 1856, 1857, and 1865 explicitly contrasted the proverb "A green Christmas [or Yule] makes a fat churchyard" with a white Christmas (or Yule).
The United States seems to have arrived late at the "white Christmas" party, with an 1849 instance of the term the earliest I've been able to find. It seems quite possible that the adoption of "white Christmas" occurred independently on each side of the Atlantic, but if the expression migrated from one coast to the other, it almost certainly migrated from east to west.
