There is a Western custom of having a look at the Annunciation (and often also the Visitation) in the run-up to Christmas. The instinct for this is an obvious one, and led to the special celebration of our Lady in the Ambrosian Rite on the last (sixth) Sunday of Advent. Similarly, the Roman postconciliar 'reforms' made Advent IV a Marian celebration; not unintelligently, once you have conceded the everything-into-the-mixing-pot model of liturgical 'reform'. For, although in one sense it is rational to make the Annunciation precede the Nativity by nine months, in another sense the mind naturally groups together events which are inextricably bound together, and wishes to revisit the Annunciation while its thoughts are occupied with the ventura sollemnia of the Birth. I will attempt the briefest summary of what the Roman Tradition has to offer.
Old Rite EMBER DAYS
The December Ember days, originally apparently associated with the Olive Harvest, were soon transformed into preparations for Christmass. The old mass for the Wednesday in the week before Advent IV, beginning Rorate, has the Annunciation for its theme (the Friday mass commemorates the Visitation). Slightly adapted, this became, in the Old Rite, the Advent Votive of our Lady (translation in the English Missal).
Appendix pro aliquibus locis
The old nineteenth century Supplement under this name has a feast Expectatio Partus BMV on December 18. It combines Advent elements (such as the Rorate introit) with things from March 25. Incidentally, England was one of the very many countries where it was on the local calendar, back in the days when the Holy See had granted a Calendar for England and before it replaced it with different Calendars for the respective RC dioceses (I wonder when that was?).
This feast, which one might have assumed to be an agreeable piece of Hispanic baroquery, is in fact quite old; it is said to date back to the Xth Council of Toledo in 656, when the Spanish bishops ordered a Feast of the Annunciation just before Christmas. This was partly because of its inherent thematic suitability, partly because the feast on March 25 is either overshadowed by Lenten themes or (when transferred) confuses the days after Low Sunday. The Spanish feast had an Octave leading up to Christmas itself, during which there was a daily High Mass attended by expectant women.
New Rite WEEKDAYS
The Roman Revisers who created the Weekday Eucharistic Lectionary (which is also authorised for use in the Church of England) made the Gospels for December 20 and 21 the Gospels respectively of the Annunciation and the Visitation (vide also the Collectio of Marian Masses). Additionally, they provided Votive Masses for our Lady, a different one for each season. The Advent votive begins with a translation of the Introit Rorate. If you used, from the selection offered, the Reading from Isaiah 7 and the Gospel of the Annunciation, you would have a close modern approximation of the ancient Mass for the Ember Wednesday. (Those who confine themselves to Common Worship could simply use the Mass provided for March 25 with appropriate Marian hymns.)
"THE RORATE MASS"
A beautiful custom arose in Germany and Eastern Europe of saying an Advent Votive Mass of our Lady in the darkness just before dawn, entirely by candlelight. As well as being very ancient and very suitable to the few days before Christmass, it also comes round about the time (in the Northern hemisphere) of our shortest day. It thus has pastoral potential just when the human frame and psyche need to be cheered up by the prospect of lengthening days and the return of Light.