Why So Many?

Yes, there are a LOT of strange beings associated with the Winter Solstice... but the variety may not be anything more than a reflection of each individual place creating it's own personalization of the idea of the Giver and Punisher. From what I can see at the moment -- and we'll see if research changes this later -- there seems to be two main factors for predicting where the Givers and Punishers will appear.

First, they appear to be only in areas with life-threatening winters... the closer to the equator, the less these beings appear to have been reported (no matter how popular reports of Santa Claus are now!).

Secondly, they seem to appear mostly in areas where there was a cultural conflict between an incoming Christian religious system attempting to re-write or erase earlier non-Christian beliefs and practices in the areas. Christianity as a belief system has always had an emphasis on the idea of a conflict between good things and bad things, and judging people based on these ideas; and that's pretty central to most of the beings I've noted so far.

As far as I've seen (and, again, this might change as I find more examples) there are no reports of these Givers and Punishers in areas without lots of snow -- Africa and South America, for example -- and we don't see them in religions older than Christianity -- Judaism, for example.

These premises need to be tested, of course; I'll keep digging into folklore from many countries to see what I can turn up. I'll double-check Africa and South America, India, China, and so on to see if viable other Winter Solstice Givers and Punishers can be found in unexpected places!