that's not the question to hand. winter solstice is the shortest day -- at first blush you'd think it would be the coldest, having gotten gradually colder as the days shorten, and that the weather would be on the upswing from there; but that point comes one month later. that's the lag.

The friction that the surface of the planet has to give to the atmosphere takes awhile to... ahem... *take* - (I suppose, in this case... *give).