If you're puzzled about why the celebration was several days after the winter solstice, which occurs at about December 21st every year, it just takes a bit of watching shadows.
As you know, the winter solstice is the shortest day of the year. It is the time when the sun is at its very lowest in the southern sky. And if you start watching the days getting shorter and shorter, you can't be blamed for starting to worry. I'm sure that the horror of thinking that the sun would continue to get lower and lower, and the days get shorter and shorter, until the sun was gone forever, was not lost on my ancestors in northern Europe.
So, if you watch the shadows on the day of the winter solstice, you see that they are very long as the sun gets to its lowest point in the south. And the next day looks pretty much the same, as does the next day, assuming you are just looking at a stick on the ground, which is about all my ancestors had thousands of years ago.
After a few days after the winter solstice, the shadows coming from the south begin to shorten. And just to be sure, you wait, maybe allowing for a several cloudy days. Sure enough, the sun is coming back. The days are going to get longer again. Life will go on. It's time for a great celebration!