Although the first day of winter arrives in late December each year, many regions of the country don't see their coldest weather of the season until later in the winter. This can seem counter-intuitive since the first day of winter is the day that offers the least amount of daylight of the year. However, other factors come into play that push the coldest days of winter weeks after the first day of the season.
The image link below displays what time of the winter the coldest days of the season are most likely. This was compiled by crunching numbers from the years of 1981-2010. Notice how much of the eastern half of the country doesn't experience the coldest days until mid to late January. Meanwhile, further west, many areas see their coldest days anywhere from mid to late December.
For the eastern half of the US, the coldest air masses of the season oftentimes don't arrive until mid to late January. These frigid air masses build in the Canadian Arctic as well as Siberia regions. When the polar jet stream dives southeast out of Canada, these bone-chilling air masses drop southeast across the eastern half of the US.
By this time of the winter there is typically more snow cover built up across the Plains over thru New England. The more extensive snow cover this time of year also comes into play due to the albedo effect. So even though the days are getting longer in January, the added snow pack reflects a larger portion of the sun's energy back up to space, thereby keeping temperatures colder over the snow pack. This allows for the frigid air masses to stay much more intact than they would if they were building into areas with little to no snow cover.
Check out this graphic to find out when the coldest days of the winter can be expected where you are!