Frogs and toads do not normally eat mosquito larvae, neither do their tadpoles.
http://sciencing.com/eats-mosquito-larvae-8156460.html
From this article:
"FROGS, TOADS AND TADPOLES
Adult toads and frogs will consume the adult mosquitoes, but they are not a major part of their diets. Tadpoles of some frog species will eat the larvae if nothing else is available. Tadpoles will also compete with the larvae for food. The competition makes it difficult for the larvae to consume enough nutrients to mature."
Granted, tadpoles are herbivores and only start eating "bugs" as they get close to emerging as toads/frogs.
The article also said that certain water beetles and dragonfly larvae [among others] would prey on mosquitoes and the larvae.
With the surrounding vegetation, you're going to have a fair amount of organic material falling into the pond so if you don't want to provide water movement, you'll need a substrate with a submerged plant population that can help process those organics.
Submerged plant population, like what we put in our ponds? Hornwort, stuff like that?
OK, I'm starting to see a pattern here......
To combine what
@Meyer Jordan's article said about predator insects, and what
@MitchM said about the organic material..... This is what I've noticed when I leave containers out that contain [pulled or left-over] pond/bog plants: there is a good amt. of organic matter on the bottom, but the water on top is clear. Clear, until I stir it up, that is. And I will find all kinds of critters that have called the organic matter home. This water never has an odor, even when disturbed. Usually there will be bits & pieces of maybe some hornwort or anacharis floating around in the water -- that had maybe gotten stuck in the plant roots, or tossed in because they were too small to put back in the pond.
And while I'm constantly emptying pots and things in the yard that are filled with rainwater AND which DO contain mosquito larvae, the "accidental bogs" that are left unattended never do have skeeter larvae..... Hmmmm.......
Keep the suggestions and comments coming! I will look at all possibilities.