Regarding the winter solstice
I have not heard anything about a tree on top of the house in Scandinavia either.
Before Christianity in Sweden the juldrickandet - yuledrinking - which is the only tradition which actually is written down was some place at the end of october until middle of January. That sounds very practical as harvest, slaughtering and other farmer things were finished. But this celebration could also have happened between November 14th and December 14th and might have had something to do with solstice.
Year 425 BC solstice was the 25th of December. But the time moved slowly over the centuries.
Year 325 it was the 22nd of December
Year 11oo it was the 15th of December
This was changed in Sweden to the more correct gregorian calender year 1753.
So now wintersolstice is the 22nd just as year 325.