In the United States, we don't literally recognize the solstice itself, but Christmas is a complicated mix of traditions and is <em>partly</em> a celebration of the solstice. Although traditionally, as the name Christmas indicates, it is celebrating the birth of Jesus Christ, in historical fact Jesus was born in the springtime. It is often thought that the traditional date of Christmas, close to the time of the solstice, was chosen to make it coincide with existing non-Christian traditions like the Roman Saturnalia.

Christmas is a rich mix of elements from Christian and non-Christian traditions. Some of it derives from the Roman Saturnalia, some from pre-Christian folk traditions (the "Christmas tree" is an old German folk tradition unrelated to Christianity). (And unfortunately it has always been the subject of controversies between those who wish to emphasize or minimize various aspects of it).

Newscasters will always mention that "today is the shortest day of the year" and in polite small-talk it is common to mention it, just as one might mention the weather.

In Japan, we have a bath with a citrus fruit called yuzu, and eat pumpkin or some other food such as rice gruel with azuki beans and konnyaku. Even the capybaras in zoos have a bath with yuzu!

I'm from Mexico and here we don't have any custom today, but I think many Mexicans ate dumplings today but not for a custom jeje