I believe they might have meant that it comes in October/November, not that it's gone by December. It stays "miserable" until spring, with January and February being the coldest and snowiest.

The point is that just freezing cold is not miserable. Autumn weather with days getting very noticeably shorter and it’s cold but not freezing and gray for weeks is quite depressing for many. In contrast, proper winter with snow and days getting longer feels much better even if you need warmer clothes and more heating. This year and next will be a bit different as everyone will be very conscious about gas prices, but purely from weather perspective early December is the worst.

> The point is that just freezing cold is not miserable

I think the fact that what is most "miserable" to people varies so much is why trying to use the names for seasons to apply to whichever weather you dislike the most is confusing. I prefer the cold to the heat, and I'm much more miserable in hot humid days due to sweating than I am in the cold when I can bundle up and feel mostly fine, but it would be absurd for me to refer to June through September as "winter" in the northern hemisphere based on this.