It is indeed end of November in the actual Russian text and all my research so far shows that this is a genuine author's mistake.
"Он исписал альбомы девочек стихами и нотами и, не простившись ни с кем из своих знакомых, отослав, наконец, все сорок три тысячи и получив расписку Долохова, уехал в конце ноября догонять полк, который уже был в Польше."
At least one more English-speaking person had spotted this back in 2006:
- It's the third day of Christmas holidays; Nikolai and Denisov plan to rejoin their regiments after Epiphany (January 6 by our calendar).
There's dinner, a ball, a couple days go by, gambling, Denisov leaves,
Rostov stays on a couple weeks, then leaves at the end of November.
This mistake is also mentioned in this work by L. Saraskina about Dostoevsky's "Demons". The translation is available here. Here is an excerpt:
Action of the novel War and Peace begins in July 1805 and ends in
December 1820. Fifteen years of life of Tolstoy’s characters unfold
against background of universal historical events with which they are
most closely connected. This connection actually determines the
internal chronology of the novel: all episodes connected with wars,
battles and other historical events are dated exactly, literally up to
an hour. When, however, the narration deals with characters’ personal
lives the chronology can be sufficiently approximate: “in the middle
of Winter”, “in Summer”, “in the beginning of Fall” and so on.
The calendar is sometimes intentionally1 imprecise. Here is one of the “peace” episodes: having lost in cards to Dolohov forty three
thousand rubles during Christmas holidays (in the text it is indicated
even more precisely: two days after the third day of Christmas, in
other words on December 29), Nicolay Rostov “spent two more weeks in
Moscow …and …having sent, finally, all forty three thousand and having
received Dolohov’s receipt, he left in the end of November in order to
catch his regiment.”
Chronology is sometimes respected only in relation to one particular character but does not correspond to life circumstances of
other characters. For example a surprising appearance of Andrey
Bolkonski, whom everybody considered dead, at his father’s house in
this very night from 19 to 20 March 1806, when his son will be born
and his wife will die, is almost a miracle. Princess Mary is afraid to
believe this miracle: “No, this cannot be, this would be to
incredible”. Prince Andrej, seriously wounded in the battle of
Austerlitz around twentieth of November 1805 was left to the care of
local residents. Four months that took his recovery and the old
prince’s search for his son considered missing seem to be a realistic
period of time and in this sense the date of prince Andrej’s return is
not surprising. The author had to go against the low of nature,
however, in order that his character had time to arrive at such an
important moment. We remember that the little princess, Andrej
Bolkonski’s wife, was heavy and clumsy, wearing a special dress and
not going out “because of her pregnancy” already in July 1805 in the
salon of Anna Pavlovna Sherer. She gives birth nine months after, in
other words in March 1806. It would mean, however, that the condition
that was supposed to prevent princess Lisa from going out could not
yet be so noticeable and important.
1 An important bit about the above translation is that the word "заведомо" has been translated as intentionally, which is an arguable choice. I believe that "заведомо" here was used in a sense of definitely, obviously.
As a final remark, it appears that the novel does contain quite a lot of mistakes of all sorts, this particular one being so minor compared to the others that few people noticed it.