Yes, the first day of winter is a big deal, because it's also the winter solstice. The first day of winter means that the last day of winter is on its way. With it also being the winter solstice, the days only get longer from here on out. To people who think that winter is too long, that is great news.
We need to know when the seasons change as the environment changes around us. Certain animals and plants behave differently around this time of year and it may be a signal for many people to prepare for change, whether it be in resources or outside weather. Even though we feel the change, knowing the actual season changes marks this change.
Although most Western cultures have gravitated away from pagan rituals our own holidays were designed to mimic them. The "first day of season" mark the solstices which are still used in the traditions of pagan based religions. Although they may not hold as much significance to the general population they are still very important to a percentage of the population.
The winter solstice simply marks the longest night of the year. While this is an important aspect of some pagan rituals it does not necessarily represent anything substantial in terms of the weather. The fast majority of the places in the northern hemisphere have been experiencing winter conditions for quite some time.