I don't know to be honest.

(googles it)

Nope.
The "Nikolaus" brings gifts, that is the only similarity.
But it is actually based on a real person, the bishop Nikolaus of Myra who was quite wealthy and gave goods to the poor.

... huh. I always thought Saint Nick was another name for Santa.

I think Santa might have been derived from this tradition of St. Nicolas, but it didn't originally belong to the christmas days.
In some southern german regions, there's no Santa, on Christmas itself the one who brings gifts is the "Christkind" (translates to christ-child) - which I think represents baby Jesus but is usually depicted more like a female angel? I'd actually have to do some research to really make sense of what it is supposed to be, even though I grew up with it :D

Sort of separate traditions that, because they happen around the same time, have grown together and gotten conflated?

It seems like that to me, yeah. But I haven't done any research into the history of these holidays, so I might be completely wrong.

Eh, we'll just call it the working hypothesis then, until someone tells us otherwise.

So how many winter holidays do you have, then? The one on Dec 6th, and the Christmas day one, and what else?

Well, we also have the advent calendar all throughout december (which is basically like the doughnight calendar on here) and the advent sundays, which are the last 4 sundays before christmas where we successively start lighting one more candle each week on the "Adventskranz" (don't know the english name, sorry). That's a wreath made from fir branches and decorated with the 4 candles and some small ornaments. We have a ribbon bow, a tin rocking horse, a slice of dried orange, a cinnamon stick and a fir cone on ours.
Then there's also a holiday in the beginning of January about the three wise man (or whatever they're called in english) that visited baby Jesus in the crib. But that's mostly celebrated by catholics, which I am not, so I don't know so many details. But there's kids going around blessing houses and singing songs for people while being dressed up as the wise men.

Hm... That's all I can think of right now.

sounds like a busy winter! I like the notion of the wreath adding a new candle each week. Are they seven-day candles that actually burn the whole time? Those are so fat and heavy, though, I'm not sure how you'd stick them on the wreath....

Well, all the candles are on the wreath right from the start, we just don't light them yet.
But no, we just light it when we sit down at the table, usually. I'd be too worried about the fire to have any candles burn while I'm not near them. And I mean, the first candle would need to burn for four weeks, so I guess it'd need to be huge... Don't think that would work.

That, or you could replace it..

So you just burn one candle a week, and which candle depends on each week?