The title is pretty much all for the question - what I want to know is what are the months, how long are the months, how many of them are there, in Westeros.
Has it been mentioned in the books? Since in the TV show I haven't ever seen anyone mention the name of a month. The same goes for the days in week, no one has revealed what a particular day is called.
Months exist but are not named.
In fact, in the whole ASOIAF series, the word "month" is only said 8 times. In those 8 times, a name is never given to them. My source for this count is text searching my ebooks.
We do know there are twelve months in a year and both are based on the solar cycle. However, GRRM does not go the one step further and tell how many days are in a Westeros year.
Days are likewise not named in the series, but a day is fairly easy measure; sunrise to sunrise
In universe the Maester do seem to study the passage of time in at least some detail as at least two books have been written on the matter:
Maester Nicol's, "The Measure of the Days"
Maester Nicol's The Measure of the Days—otherwise a laudable work containing much of use—seems influenced by this argument. Based upon his work on the movement of stars in the firmament, Nicol argues unconvincingly that the seasons might once have been of a regular length, determined solely by the way in which the globe faces the sun in its heavenly course.
Archmaester Walgram's, "The Reckoning of Time".
One issue that plagues all studies of the ancient records is how differently the varied cultures reckon days and seasons and years. Archmaester Walgram's great work, The Reckoning of Time, delves deeply into this problem, but there is little consensus on what the dates we have actually mean in our own reckoning.
