Well, as to why we call the Christmas celebration a "midwinter" festival... that's really a cultural thing.

According to our current culture, the start of winter is defined as the winter solstice -- the day on which the sun's path appears cross furthest to the north of the celestial equator. This is also the day with the shortest amount of sunlight per 24-hour period, give or take a minute or two.

But in other cultures (such as the ancient Celts, for example) the start of "Winter" was on or around what we now think of a November 1st -- the ritual day on which the herds of cattle were brought down from their summer pastures in the mountains, and the start of "Summer" was when the cattle were brought back to the mountains on or around May 1st. Defined in this way, the end of December is much closer to being "midwinter".

As for why Mrzzy wants to celebrate (Whateverday) at this time, he (you are a 'he', right, Mrzzy?) did state that this was the one time the whole family could actually get to together -- logistics can't be dismissed too easily :-).

Also, for the atheistic, agnostic folks out there (who might also be science-minded, or they might not be), the Winter Solstice is a measurable moment -- something that happens for simultaneously for everyone living in the northern hemisphere. So, if you're going to pick a particular around which to center a celebration, it's an easy one to decide on, rather than trying to decide which week in February is the gloomiest...