As others have said its based on Earth's orbitlal tilt. These occur on fixed dates. Of course what the actual weather is like that day varies drastically so you can assume for example that the actual season weather-wise starts these dates. It would be impossible because the weather varies from year to year and place to place!
However, the dates of the solsticies and equinoxes are not fixed. Over thousands of years they change so the dates will have to change to reflect this fact. Eventually the hemispheric solsticies will swap dates! Ie northern hemispherw inter will start in June insteasd of December and vice versa for the southern hemisphere.
So they will have to be changed or else it will make no sense!
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.