Actually, the sun doesn't work its way anywhere. The solstices are an effect of the motion of the Earth, which, of course, revolves around the sun. Since the Earth's rotational axis is tilted with respect to the Earth's motion around the sun, there is a point in the Earth's orbit where the Earth's northern hemisphere is pointed a little bit toward the sun. Sunlight then falls on the northern hemisphere more directly, and we northerners call it summer. Six months later, the Earth is on the other side of its orbit, and the northern hemisphere is pointed away from the sun.
Sunlight falls at an oblique angle, and the sun appears low in the sky.
Sunlight doesn't heat things very well when it comes in at such a low angle, so everything cools off. The extremes of these two situations are the solstices. And yes, if the northern hemisphere is pointed away from the sun, the southern hemisphere is pointed towards it, so December is summertime for our friends down south. June down there is jacket season. In previous eras, the winter solstice was a time of great celebration in Europe, the Americas, and elsewhere.