While I think a lot of people believe that winter begins as soon as they see snow, or summer is over as soon as the weather cools, it is important to remember that the dates marking when a season changes from one to the next are based upon the Earth's orbit.
The start of winter should not be changed. First of all, the date is based on science and the solstice. This science will not change. Why would the start of winter be considered for change? For the school calendar or for weather? All of these are particular to the area that a person is in.
The first day of winter is set according to the lining up of the earth, the moon, and the sun. I don't know the exact science, but I do know that changing the date doesn't make any sense. The beginning of winter happens because it's the shortest day of the year, and that is how we know it to be.
So many religions out there are recognized as legitimate yet some of the oldest to exist are still widely disregarded. The dates that mark the beginning of the seasons are determined by the solstices. If we change the dates arbitrarily it is a disrespect to those who observe solstice traditions.