Some years ago, researchers began looking into the astrological theories of the Celts based primary on Robert Graves' work, The White Goddess. Foremost in this research has been Helena Patterson, whose two books, The Handbook of Celtic Astrology and The Celtic Lunar Zodiac, are considered by many to be the definitive works on the subject.
However, since the Celts were an oral tradition society, rather than a written one, Druids left no written records describing their mathematics or techniques, aside from Oghams - glyphs. This makes a definite translation of Druidic/Celtic astrology into Western terms a difficult proposition at best. Additionally, a number of experts in early Celtic history seriously dispute the accuracy of Graves' work and thus any research deriving exclusively on Graves' research must be considered suspect. More on this: The Fabrication of 'Celtic' Astrology by Peter Berresford Ellis
Thus, according to Graves: The Celts and Druids used a 13 month Lunar based calender (This may have been similar in many ways to that used by the Chinese) rather than a Solar calender. (The Gregorian calendar is Solar based, with the year roughly divided into twelve more or less equal parts and built in provisions for the necessary calendary adjustments needed to bring it in line with the real world*.
Patterson's study, based on the writing of Robert Graves indicates the Celtic year was more or less evenly divided 13 months, with the New Year beginning 3 days after the Winter Solstice. (This time was referred to as Dragon days - the darkest time of the year, when the forces of darkness held sway, to be finally beaten back by the light of the returning, reincarnated, Sun (or Son.))
Patterson and Grave's work aside, researchers have not yet determined (that I have found) how (or if) the Druids made corrections to their lunar calendar to bring it into line with reality, or whether they based the beginning of their year on a Solar cycle, as Patterson suggests, disengaging their Lunar calendar from the cycles of the Moon in the sky.
To complicate matters, John King, in his book The Celtic Druids' Year - Seasonal Cycles of the Ancient Celts disputes Graves' placement of the New Year Day with No-Name at Midwinter on the grounds that Roman writers quite definitely state that the Druidic Year began in high summer and that in terms of the metaphysical birth-death cycle of the old-new gods represented within the calendar a mid-summer new year makes better sense. Therefore, with apologies to Celtic scholars and in keeping with King's analysis:
The Birch Tree Dec 7- Jan 3 Midwinter
The Rowan Tree Jan 4 - Jan 31
The Ash Tree Feb 1 - Feb 28 Imbolc
The Alder Tree Mar 1 - Mar 28
The Willow Tree Mar 29 - Apr 25
The Hawthorn Tree Apr 26 - May 23 Beltane
The Oak Tree May 24 - Jun 20
And a Day Jun 21
The Holly Tree Jun 22 - Jul 19
The Hazel Tree Jul 20 - Aug 16 Lughnasa
The Vine Aug 17 - Sep 13
The Ivy Sep 14 - Oct 11
The Reed Oct 12 - Nov 8 Samhain
The Elder Tree Nov 8 - Dec 6
There is evidence that the tree names applied to the Oghams by Graves are also in error. That some of them, in fact, relate to other Celtic words not at all related to trees and that other words have had their meaning stretched beyond reason. As I am not a Celtic scholar, I cannot address these issues. However, Peter B. Ellis's research into Celtic astrology indicates the early Celtic calendar and astrology has close similarities to the Vedic astrological system. And Michel-Gerald Boutet discusses this in depth: DRUUIDICA PRINNION (Druidical Astrology).
*There are 12.3 (approximately) lunations per solar year. The Chinese handle the discrepancy by adding a 'Leap Month' every three years. The placement of this month in the calendar is determined by a traditional rotation.