Since it’s the shortest day of the year you would think it would be the middle of the col season, as the days get longer after.
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Our season naming convention largely has to do with agriculture, and northern hemisphere temperate agriculture too. So it’s not necessarily accurate to winter conditions everywhere.
However in Europe, by the equinox virtually all harvests are complete and no more will take place. Nothing new grows and everything hibernates. The coldest weather also follows as the limited amount of sunlight drops the average temperature until the days are long enough to heat up. So the coldest, darkest, and least fruitful months are labeled as winter. When things usually begin to sprout and grow again is called spring.
Because the Earth holds a lot of heat. It takes time for that heat to transfer in or out; the same way that, upon lighting a stove, the pan is still cold to touch, and after extinguishing the stove, the pan is still very hot but has just started cooling down.
The speed of heat transfer is correlated to how hot the object is. So even though the days are getting longer again, it’s not enough to actually keep the planet warm; the planet is “too hot” and therefore transferring heat away (to space) too fast for the small amount of sunlight (even though it’s slowly increasing) to make up for it. By the spring equinox (~March 21st), there’s enough sunlight on the hemisphere to steadily warm it up, which leads to spring and summer.
Seasonal lag.
The atmosphere is actually pretty complicated and chaotic, but at its core atmospheric phenomenon (like temperature) are determined by energy inputs. One of the major players in determining the temperature is the ocean.
The sun provides energy to the earth, and much of that energy is transferred into the atmosphere–so the sun (and thus the amount of sunlight, and thus the length of the day) does play a significant role. But water retains heat very well and lets it out slowly, so even as the days get shorter, the ocean is still releasing heat back into the atmosphere. It takes a while for this giant store of heat to run out, so there’s a bit of lag between when the days are shortest and when the temperature is coldest.
Then, when the days start to lengthen again, the ocean sucks up a lot of that heat–so even with longer days, the temperature doesn’t really begin to rise much until the ocean temperature does.
The result is a seasonal cycle that’s just a bit off from the daylight cycle.
There are meteorological seasons and astronomical seasons. Meteorologically (based on temperature cycles) the seasons are divided into three-month blocks. Winter is Dec, Jan, Feb; Spring is March, Apr, May, etc. Astronomically (based on the earth’s position relative to the sun), Winter is approx Dec 21 – March 19; Spring is March 20 – June 20 and so on.
Lets say you have a piece of metal and a blowtorch, When you put the blowtorch on the piece of metal it takes a few seconds to a few minutes to heat up to the point where its losing heat to its environment as fast as you’re putting heat in with the flame.
Now turn the torch off, the temperature likewise doesn’t instantly cool back down to the starting temperature, it takes a while.
The same is true of the earth and the sun, just on a much bigger scale. The coldest and hottest days are when the heat in and the heat out are equal. The rate heat comes in depends on the amount of sunlight received, the rate heat goes out depends on the current temperature.
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