Feeder guppies work well as long as the water is warm enough. For cooler water you can try danios (zebra danios or the glo-fish tho those are genetically modified), white cloud mountain minnows or rosy reds (they
sell them as feeders but they are just a color morph of fathead minnows).
Fish don't really need aeration. As part of a home school
project we raised fish in outdoor tubs and kiddy pools for the last several summers. Never aerated. They mostly thrived. The things you need to watch out for are the temperature fluctuating too much and the water drying up (in your case). With guppies or a betta fish (and if you go that route get a female - cheaper and swim better so they can eat more) you can just scoop them out if the water looks like it will dry out and put them in a
bucket of (dechlorinated) water until it rains again. Keep them indoors over winter or give them away and start over in the spring.
Rosy Reds and feeder goldfish can survive being in water with a lot of ice in winter. I had a goldfish locked in solid ice that thawed and started to swim again in the spring!
Any of those will eat mosquito larvae, but the betta would probably eat the most. Goldfish need more room than the others or they'll cause ammonia levels to spike (ammonia is fertilizer so if you're using the water for plants that could be a good thing!)
Another possibility is killifish. Some of them are adapted to live very short lives in puddles that dry up. The eggs are sold dry and you put them in the pond to hatch them. The babies grow phenomenally fast, breed, lay eggs until the water dries up and once the pond dries up that prepares the eggs to hatch next rain. Because of the very fast growth rate they eat a LOT of live food. They are territorial, and will fight to the death after they reach a certain size, but you can scoop the excess and sell them to a pet store (they love novel kinds of fish and killifish are very brightly colored). You can find them on aquabid.com or ebay.com.
If you decide to get feeder guppies, they often sell for 10-15 for $1, but the stores rarely see them mature, at which time they get really neat colors. I've sold them back to the pet stores as adults for $1 each as "Endler's Guppies" (wild type), which is what they are. If they only want to trade with you, you can use the credit for sunflower seeds to plant next spring.