It is not enough to have cloud drop nucleating materials such as hydroscopic SO2 in the air. Those nuclei help form liquid water droplets in the air but won't help getting the ice crystals built and harvests the 80 calories released on each gram of water frozen. Between 0 C and -40 C there have to be ice nucleating materials present. Sea salt doesn't do the job until you get the cloud drops super-cooled down to at least -35 C.
Before we get to the juicy stuff on decomposition of organic matter we need to ask the question: What is the big deal about freezing anyway? Well, when the phase change between liquid water to solid water takes place, about 80 calories per gram are released. With this heat, air becomes warmer and more buoyant, and updrafts more violent. In addition, cloud drop growth is quite slow if there is no ice nucleation. If there is ice present in the air, the ice steals the water in the liquid drops and so the ice particle grows rapidly at the expense of the liquid drops.
Here is another answer to the what's-the-big-deal question. For water to fall out of the sky, the drops have to get to be big enough. When they are small, like in a fog, they just hang around as a sort of suspension. Sort of like the suspension of egg yolk in vegetable oil, i.e. mayonnaise. Clouds are such a suspension, although lower in diet calories.
So, how do you get all those little drops to get bigger and fall out of the sky? Well, if you add a few drops that have ice-nucleating stuff in them and the temperature gets low enough, an ice crystal forms. Now we all know that the vapor pressure over water is greater than the vapor pressure over ice at temperatures below freezing! Right. So now the lucky cloud droplets with the decomposition-generated ice nuclei grow larger by stealing water molecules from the liquid water drops! The vapor pressure gradient favors ice over liquid water. So decomposition ice nuclei increases the chance of a drop growing large enough to fall to earth and of course decomposition in the soil may be fostered by such drops from above. But that is positive feedbacking about climate and biota before we are ready for it.
Proponents of this ice-mediated, drop-growth, big-enough-to-fall theory categorically state that ALL moderate-to-heavy precipitation is initiated in this fashion and that ONLY drizzle-type precipitation could fall from clouds which do not contain ice crystals. To get the Andrews LTER more bigger-drops rainfalls, we need to put some barges of rotting organic matter out to sea (oceans don't put out all that many ice nuclei on their own). There is a big east coast city with just the garbage barges you need! Rotting vegetation controls climate! Here is YET another answer to the what's-the-big-deal question.