The fuzzy texture and shade-loving characteristics of moss are in part due to it being a non-vascular plant. Mosses belong to a group of plants called Bryophytes. These plants do not have roots, or the xylem and phloem of vascular plants, but rather have rhizomes that hold the moss in place and collect water and nutrients the moss requires.

As you move away from the tropics, the suns rays intersect the earth at an angle. Here in Santa Barbara, California, the sun is not directly overhead, but to the south, so the south side of any object will get more sunlight than the north. This is why moss likes the north side of trees.

Your observation that moss only grows on the north side of trees tells me you haven't looked for moss near trees in the southern hemisphere. Moss is a simple plant and likes to grow in shady locations so it does not dry out. It is pretty simple to picture why this is the north side of trees here and the south side of trees in Australia for example. The sun's rays strike the earth's surface nearly perpendicular close to the equator.