Why do south areas of the Equator not get snowfall?

For there to be snow, there has to be precipitation in a cold climate. Lots of the areas near and just south of the equator don't get cold, so there isn't much snowfall. But there are places where there is snow in the southern regions, but that is at very high elevations. At these higher elevations, the climate gets colder and colder as you climb higher. As the temperature gets cold enough, it will begin to snow there as well.

But in general, since these are mostly warmer areas, you won't get much snowfall. The low lying areas remain warm, and whenever there is precipitation, it comes down as rain. Much of these lands just don't get enough cold weather to get the snowfall.