H.P. Lovecraft, "The Festival":
It was the Yuletide, that men call Christmas though they know in their hearts it is older than Bethlehem and Babylon, older than Memphis and mankind.
"Christmas customs in many lands", Monthly Bulletin of the Carnegie Library of Pittsburgh, December 1919:
No time in all the Twelve Nights and Days is so charged with the supernatural as Christmas Eve. Doubtless this is due to the fact that the Church has hallowed the night of December 24-5 above all others in the year. It was to the shepherds keeping watch over their flocks by night that, according to the Third Evangelist, came the angelic message of the Birth, and in harmony with this is the unique Midnight Mass of the Roman Church, lending a peculiar sanctity to the hour of its celebration. And yet many of the beliefs associated with this night show a large admixture of paganism.
First, there is the idea that at midnight on Christmas Eve animals have the power of speech. This superstition exists in various parts of Europe, and no one can hear the beasts talk with impunity…
It may well have been the traditional association of the ox and ass with the nativity that fixed this superstition to Christmas Eve, but the conception of the talking animals is probably pagan.
Related to this idea, but more Christian in form, is the belief that at midnight all cattle rise in their stalls or kneel and adore the newborn King. Readers of Mr. Hardy's "Tess" will remember how this is brought into a delightful story told by a Wessex peasant. The idea is widespread in England and on the Continent, and has reached even the North American Indians. Howison, in his "Sketches of Upper Canada," relates that an Indian told him that "on Christmas night all deer kneel and look up to Great Spirit." A somewhat similar belief about bees was held in the north of England: they were said to assemble on Christmas Eve and hum a Christmas hymn. Bees seem in folk-lore in general to be specially near to humanity in their feelings.
I've encountered various versions of the idea that on Christmas eve "no one can hear the beasts talk with impunity" . I cited a few of them in "Talking animals: Miracle or curse?", 10/24/2004 — a couple of stories focused on the idea that the animals might tell you something you'd rather not know, and another ("Bertie's Christmas Eve", by Saki) suggesting that listening for the animals might let you in for some maltreatment of human origin.
There's another version of this story (told as a story-within-a-story) in Marguerite Cunliffe-Owen, The Tribulations of a Princess, 1901:
"Ever so many years ago, when the angels had not as yet turned their faces quite away from the wickedness of the world, and when the land was not infested with as many devils as it is now, there lived in Finisterre a stalwart lad, handsome as daylight, who loved a lass, beautiful and true. But, alas! the girl's father was rich; for he owned four fields, an acre of salt-marshes, and a clump of cork-oaks, and of course he would not hear of giving his little daughter to a sailor-boy who earned but a mere pittance by risking his life day and night on the cruel sea in a cockle-shell of a fishing-boat. And so the lad and the maid were very unhappy and mourned their wretched lot when they met by stealth on the edge of the landes.
"It was Christinas Eve, and on his return from the midnight mass the lad, whose name was Marie-Pierre,went to the stable and threw himself wearily down on a bundle of straw in an empty stall. He found here a warm and comfortable spot where he could be alone with his sorrow, undisturbed by the noisy rejoicings of the réveillon.
"Fatigue, however, soon overpowered him, and he fell into a deep sleep.
"When he had slept a little while he was suddenly aroused by the sound of voices close beside him. The tones were strange, muffled, and unnatural, and filled him with a nameless terror, which he had never felt before, for he was no coward. For a few minutes he lay with closed eyes listening intently, and trying to find out who had spoken. Meanwhile he trembled sorely and searched mechanically for the rosary in his pocket, to preserve himself from malefices.
"An uncontrollable curiosity at last compelled him to raise his head cautiously and to look up. The barn was dimly lighted by a great horn lantern, but his sight was rendered so acute by fear that he could see almost as well as in broad daylight. Again and again he glanced into every nook and corner, but could discover no one in the stable. Only the cattle stood near by, knee-deep in thick litter, yet a voice came from a stall near by. The occupant of this stall was a very aged ox, kept on the place more in gratitude for his past services at the plough than with any idea of possible further use. Marie-Pierre peeped through a chink in the wooden partition separating him from the decrepit animal, and to his horror discovered that it was the old ox that was talking.
"For a few seconds he was paralyzed with amazement. Then like a flash the memory of an old legend, according to which animals are endowed with the power of speech on Christmas Eve, between midnight and daybreak, rushed through his mind, and, though a cold shudder shook him, he resolved to keep absolutely quiet, so as not to lose a particle of what was going on.
"When the ox had completed the sentence which had awakened Marie-Pierre, the thread of discourse was taken up by an equally antiquated donkey at the farther end of the stable.
"'Ah!' exclaimed the latter, 'how blind men are not to understand the true ways of nature! If they were, for instance, told that we are able, on Christmas Eve, to speak as well as they do themselves, they would only shrug their shoulders and laugh in scorn at so preposterous an idea.'
"'Men only care for us/ retorted the ox, sententiously, 'because we help them to earn money. Money is all they care for! Yes, yes! money alone, and—aha! if they only knew it—I, old and feeble and despised as I am now, could tell the wisest of them where undreamed gold and riches are to be found in such abundance that—'
"' What on earth are you talking about, old friend?' interrupted the donkey. 'You must of a truth be getting on towards your dotage to tell such extravagant tales, or else the clover and Christmas oats have gone to your head.'
"' Laugh away/ exclaimed the ox, extremely nettled by the donkey's remarks. 'But, for all that, I can assure you that during the Vigil of St. Sylvester, once in every hundred years, at the stroke of midnight, the old Druidical stones of Plouhinec, a mile from here, leave the spot where they have stood during so many long and weary centuries and go down to the sea to drink their fill. Beneath the place which they leave vacant while thus doing are great pits filled to the brim with treasure, and I have been told long ago by my sire that the glitter of the stones which men call diamonds, the soft gleam of pearls, the fiery light of rubies, heaped up therein, make a halo around the spot equal to the brightest moonshine.'
"'Whew!' brayed the donkey, excitedly, 'that must forsooth be a grand sight! But how is this treasure to be reached?'
"' The treasure is unknown to humanity, for this secret has never been betrayed, and even if men knew about it they could not touch it, for the stones would rush back and crush the thieves like insects under their awful weight, unless the blood of a Christian be sacrificed to the spirits which animate these monuments of past and pagan ages.'
"As the ox pronounced these last words, a distant bell boomed forth the hour of daybreak. This was the end of the time allotted to the animals for speech, and with a deep-drawn sigh they relapsed into silence."
You can read the rest of the story in Ms. Cunliffe-Owen's own words — suffice it to say that the blood of a Christian is indeed sacrificed.
The Norwegian version of this idea suggests less concern for the talking animals than for the dangerous roving spirits:
A highlight of the season is December 13th, Santa Lucia Day. The festival celebrating the "queen of lights" is celebrated in schools, day-care centers, nursing homes and hospitals, with processions led by a young Lucia in a white robe with a crown of lights on her head and a candle in her hand. Traditionally the girls bring baskets of saffron buns to hand out.
Historically Norwegians considered what they called Lussinatten the longest night of the year and no work was to be done. From that night until Christmas, spirits, gnomes and trolls roamed the earth. Lussi, a feared enchantress, punished anyone who dared work. Legend also has it that farm animals talked to each other on Lussinatten, and that they were given additional feed on this longest night of the year.
I imagine that the talking animals business is somehow connected to the general "world turned upside down" idea of traditional winter solstice festivals, e.g. Twelfth Night:
In medieval and Tudor England, the Twelfth Night marked the end of a winter festival that started on All Hallows Eve — now more commonly known as Halloween. The Lord of Misrule symbolizes the world turning upside down. On this day the King and all those who were high would become the peasants and vice versa. At the beginning of the Twelfth Night festival, a cake that contained a bean was eaten. The person who found the bean would rule the feast. Midnight signaled the end of his rule and the world would return to normal. The common theme was that the normal order of things was reversed. This Lord of Misrule tradition dates back to pre-Christian European festivals such as the Celtic festival of Samhain and the Ancient Roman festival of Saturnalia.
But in The Tailor of Gloucester, 1903, Beatrix Potter turns the story upside-down again — on Christmas eve, the tailor's cat Simpkin makes peace with the talking mice, and the mice make the coat that the tailor is too sick to finish. And Thomas Hardy takes a similarly positive and sentimental view of the kneeling-animals meme ("The Oxen", 1915):
Christmas Eve , and twelve of the clock.
"Now they are all on their knees,"
An elder said as we sat in a flock
By the embers in hearthside ease.
We pictured the meek mild creatures where
They dwelt in their strawy pen,
Nor did it occur to one of us there
To doubt they were kneeling then.
So fair a fancy few would weave
In these years! Yet, I feel,
If someone said on Christmas Eve,
"Come; see the oxen kneel
"In the lonely barton by yonder coomb
Our childhood used to know,"
I should go with him in the gloom,
Hoping it might be so.