Just because the water looks clean, doesn't mean it is. You won't see ammonia, nitrites, or nitrates in the water. And, snails don't eat poop....nothing will. Snails will eat mostly algae, and then will move on to any uneaten food or anything decaying on the bottom. But, it's not a good idea to leave anything rotting on the bottom. This will produce ammonia and kill off your animals.
Filters generally provide 3 types of filtration. Mechanical-which is the physical removal of wastes and solids. Biological-which is the conversion of ammonia into nitrites then into nitrates. This is done via beneficial bacteria that grows in the filter media and other objects in the tank. You must have a filter for this, because the beneficial bacteria needs oxygen to survive. And, chemical filtration-which is adding carbon and such to remove certain impurities. I don't use this one in my filters, so this isn't always necessarily going on in the filtration.
And, filters also help to add oxygen into the water. When the waterfall/filter output hits the water, it creates surface agitation. This surface agitation is what allows CO2 to escape and O2 to enter the water. Just using an air stone like some believe, is generally not enough to allow that happen, unless the air stone is close to the surface causing enough surface agitation.
All fish and frogs need a filter. The only exception would be the labrynth fishes-bettas, gouramis, paradise fish, since they have a special organ that allows them to breathe at the surface. However, they really should have a filter as well, for all the above reasons, and when they sleep, they do take in oxygen through their gills through the water.
So, just spend the few bucks, you can get a somewhat decent filter for your tank for about 10-15.00. For a few dollars more, you can get a better quality one-I would do that, and go with a Penguin/Marineland or an Aqua Clear. Also read through this link, will give you more info on the biological part of the filtering. Good luck!
http://freshaquarium.about.com/cs/biologicalcycle/a/nitrogencycle.htm
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