Well, firstly, even with your clarification of Western Christianity, we're still talking myriad cultures over 2000 years. Christianity has never been culturally monolithic, with all practices being observed exactly the same way everywhere in the world. Traditions vary from Church to Church, Country to Country, Province to Province, and Diocese to Diocese. As an example, yesterday the Catholic Church celebrated the Feast of the Immaculate Conception. In the United States, this was a Holy Day of Obligation, where Catholics are required to go to Mass. In most the rest of the world, it is still a feast day, but not obligatory. I will be discussing primarily the Latin Rite of the Catholic Church, as (a) it has the longest history in the West, and (b) it's what I'm most familiar with.

Western Christianity consists of several rites historically (not even taking into account the various Protestant traditions), such as: the Roman Rite (what most people think of when they hear Catholic), the Ambrosian Rite (still used in Milan), the Aquileian Rite (defunct, from around Aquileia), Rite of Braga (Portugal, still used rarely), the Durham and Sarum Rites (defunct, England), the Gallican Rite (defunct, France), the Celtic Rite (British Isles, defunct), the Mozarabic Rite (celebrated currently in some parts of Spain), and the rites of various religious orders, most of which are now defunct with the notable exception of the Carthusian Rite. Also of note is the Anglican Use, which is used by Anglican Churches entering communion with Rome. Each rite/Use has its own traditions associated with it.

Now that we've set up the background, let's actually examine your question. I'm not exactly sure what you mean by "Christmastime." As part of the liturgical year, Christmastide, as it is properly called, begins on the evening of Christmas Eve and extends to the Feast of the Baptism of the Lord, which falls on the first Sunday after the Feast of the Epiphany (this year, it falls on January 11). If you are referring to secular practices (such as the current trend of playing Christmas music starting anywhere between Halloween and Thanksgiving in the United States), it would be good to specify which country and which time.

From a theological standpoint, Advent is still, in the eyes of the Catholic Church, a penitential season, as signified by the use of purple vestments, excepting Gaudete Sunday (3rd Sunday of Advent) which uses pink vestments. Likewise, the Gloria is omitted. Many practices closely reflect those of Lent, and from as early as the fifth century, was known as St. Martin's Lent: a period of fasting. That being said, while it is a season of penitence, it is a joyous penitence. Think of it as cleaning before a big party: the house must be made ready (let's be honest, who doesn't find that a chore), but with the hopeful anticipation of the guests' arrival. It must be done, and it may be dull and dreary, but there's something to look forward to in it.

The earliest hint at the origins of Advent is from a synod in Saragossa in 380 that required from December 17 through the Feast of the Epiphany that the people attend church. There are further hints in the writings of St. Caeserius in the early 6th century, but nothing definite. We get our first real hint of it from a Synod in Gaul (Macon) which required that between November 11 and Christmas, the Mass should be offered according to the Lenten practice. Various other synods required fasting until Christmas beginning anywhere from the Autumnal Equinox to November 15.

Advent was, from its earliest inception, a penitential and preparatory season, and remains so in liturgical practice. Practices vary across time and space. As to why it has changed in various locations to have celebrations before Christmas, I feel like it's such a cultural question, that more specifics are needed.

By "Christian culture" do you specifically mean Christians themselves or cultures where Christianity is the major religion? In many modern churches, advent services mark the season with somewhat sombre reflection, longing, and patience. Christmas' celebrabratory spirit continues into January; rather distinct from Advent.