Snow is actually more contaminated than rain water. The flakes have a much larger surface area for collecting icky stuff on the way down.
Lye will kill pretty much everything in rain water, except particulates like chemicals (which aren't alive) and microbiol spores (or cysts). Spores are VERY hard to kill, nigh impossible in a non-laboratory environment. They are also the worst possible form of microbial contamination. Spores are responsible for a large majority of water borne and hospital borne illness. They could potentially live through the lye, saponification, and the cure and be left on a person when they use the soap. These little things have survived INSIDE rocks that formed from volcanoes 2 million years ago. Scientists collected them and introduced them to media (a food source, usually agar nutrient gel) and the darn things "hatched" and grew colonies of bacteria. They "hatch" when they have a food source, like dead skin cells on a human for example. These are found in tap and bottled (spring or filtered) water. The distillation process is impossible for the spores to travel through, as it requires a condensation step and the spores are too large to travel on water particles in the air.
Cities deal with these by chlorination, fluoridation, and huge UV light banks that drinking water travels through. Well water that tests positive for them must be run through a filtration system. Sometimes they still get through though. Giardia is a common infection caused by micro cysts that manage to get through the precautions in water treatment.
Okie, I'm done now LOL

Can you tell I love microbiology?
