Reposting, because I forgot to put the word "lead" after "molten". Braintoot.
Just adding that in finland its a new year thing.
Its also and old folk tradition in Slovakia, although I don't know if it was done on christmas or new years
Okay, so this has been sitting here for 5 days, so I'll jump in and tell you what I know (I've written about this twice, once in a German and once in a Slavic (Czech) context).
I've wondered the same thing since I participated in one as a child at a New Years' party in Munich. It was with wax (as it usually is in modern times) but still referred to as "Bleigiessen" or pouring lead.
When I moved to the Czech Republic, I found out they do it too, and think it Slavic (Bavarians would beg to differ).
Both Germanic and Slavic pagan tradition were big on divination. From watching horses' behavior, to the flight patterns of flocks of birds, to throwing lots, etc, etc, etc these patterns in nature were "interpreted" to read the outcome of crops in the following year, or dangers, wars, famine, etc.
Especially in the winter solstice celebrations. Pagan traditions were taken whole-sale and made easier to swallow. I'll just let this one sentence stand, since I've written other answers on specific Czech examples, and whole books on how Czech traditions (including this one) came to be. Just note that in Central Europe you still see bonfires with feasts and roasting of whole animals in celebrations that start early and last all night.
And thusly, when I was a child we did this with a Catholic family in Germany. One poured wax (traditionally lead) into water, and the shape the now-solid substance made was interpreted (like clouds... it "kinda looks like a blob... er like a tree, no a man bending over... a dog") ..and then looked up in a book. A book which (in modern times) quaintly lays out the next year, for if your wax blob resembles a "maiden" ("close enough") or whatever shapes are actually listed in the book.
I'm going to go out on a limb here and say it originated a long time ago ...which is BS, but it clearly has prehistoric roots in paganism as part of the broader divinations. Things like throwing salt over one's shoulder are much older than Christianity too in Europe, but that's another story. But the Christianization attempts started (well, at least with the Franks) against the Saxons in the 8th Century, the Saxons then against the Slavs to the East in the 10th century, but we're talking much older. Thousands of years older---so I really can't say.
The fact that it's done in Slavic, Scandinavian, and German countries (and others? those are all I can say for sure) makes it hard to pin down where it originated exactly, but "Central or Northern Europe" sounds good to me.
I'm sure there's a much better answer out there, but after 5 days of it not showing up, you get me :) I hope this either helps, or at least gets someone else to add more specifics.
I'm juuuuuust publishing a book on Czech Christmas (it's late for the season, dammit!) which will mention all this stuff (and way more). I also did a podcast miniseries on Celts, Germanic paganism, and Slavic beliefs, all on The History of Germany Podcast ( http://podcastnik.com ) all covering aspects of this and other pagan beliefs and rituals.