The oceans are Earth’s heat buffers. Summers are when the ocean stores heat, winters are when it releases heat.

There is more land in the northern hemisphere, more ocean in the Southern Hemisphere. Summers get hotter in the north, winters get colder. This is because land does not store/release nearly as much heat as ocean.

> I always thought that the shortest day shouldn't be the first day of winter, but rather the middle

That's not just you. Every traditional calendar says the same thing.

As far as I can tell, the idea that winter starts on the solstice, when it's been winter for more than a month (unless you're in the tropics), is an invention of Hallmark or some other calendar manufacturer. It is based on nothing.

I tried reading Poor Richard's Almanac to see if it indicated the "beginning of [any season]", but if it does I didn't understand. (There is a column of "remarkable days", but it is often difficult to understand the entries in that column.)

Careful track is kept of the exact time of sunrise and sunset, and of what kind of weather to expect ("rain"; "snow"), but the seasons don't seem to be labeled explicitly.

There was indeed a calendar change just 4 years after the 1748 almanac you were reading. In 1752 the American colonies switched from the Julian to the Gregorian calendar. That leaped 11 days ahead.

https://en.wikipedia.org/wiki/Adoption_of_the_Gregorian_cale...