Ants love dry, compacted soil or old fallen logs. Sounds like you may have more of the former environment. Mulching will help substantially.
Frogs are great to have, but they will not put a dent in an ant population. The queen can lay 2,500+ eggs a day. A hungry toad may eat 1/20th that, and only those ants which wander above ground. You should encourage frog habitat, but it's not a solution to the ants.
You will find however, the best habitat for frogs is bad for ants. Standing pools of water for example create a barrier for ants.
Frogs are extremely vulnerable to any poisons. Much more so than the ants. As such, I would avoid sprays and granules.
For taking out individual nests, I like to use fire. Get a flame thrower! If you happen to hit a patch of lemon ants, the whole neighborhood will smell like cookies, lol. Other than that, it's a discreet method and very effective. Just bake the entrance on full blast for 30 seconds, and quench with a watering hose.
http://www.amazon.com/Red-Dragon-VT-2-23-000-BTU/dp/B00004Z2FP$40 on Amazon prime right now. + $20-30 for a 20lb propane tank. Close to what you would spend on any effective multi-application organic regiment. This also does a number on pretty much any insect pest, but it's targeted. Great for paper wasps that get too close to the house. Also an effective way to clear large areas of weeds. It's the only thing I have which puts a dent in Canadian Thistle.
This is for spot-treatment only, don't go scorched earth on the whole property, lol. That will damage soils.
Sheet mulching is your most effective preventative measure. 4-6" thick of mulch is more than ants want to deal with.
As for a small pond, don't worry about mosquitoes. The would rather breed in moist areas in tall grass or under brush. They only require about 4oz of water standing for a couple of weeks to breed. They tend not to breed in ponds if they can avoid it.
Bury a few small 100 Gallon stock tanks.
You can put some fat-head minnows in it (from a bait shop) to ensure there is no mosquito breeding. They won't bother most toad eggs, and you'll have a renewable source of fishing bait while increasing your toad population. They breed fast. If nothing else, when you make a batch of comfrey tea or other fertilizer, take a few pounds of minnows from the tank and use as a fish emulsion.
Another thing to consider, ants are not entirely bad. They have a part to play in your garden. Sugar ants are the best pollinators for many fruit species. Lemon ants are excellent decomposers of dead wood. Black ants keep grass hoppers, scorpions and cabbage moth larvae under control like nothing else. You don't want them in, or immediately near your house. But 100' away, you'd never notice them. It's really only carpenter ants and fire ants in most of the US which pose any substantial threat to property or people.
As for ant-predator species, you've either got them or you don't. I'm not aware of any place you can buy them (unlike ladybugs and lacewings). Most of the effective predators work by infiltrating the nest, appearing as food or even mimicking the queen. Once the ants carry it in, they eat all the food, eat the eggs, some just sit back and let the ants feed it like an insect welfare recipient. These basically parasitize the colony, weakening it and preventing the spread of the colony. When you kill the colony, you kill the parasites. It's been observed that destroying one colony can inflame the problem, as other ants will quickly move into the undefended territory, and their new colonies are not parasitized, so they grow very fast. Meanwhile survivors from the colony you took out will move a few feet away and begin dozens of new colonies.
As such, I would only take out the colonies which pose a problem.
