I'm going to tell you that it is possible, but there are a lot caveats.
First, a more heavily planted pool does a better job of filtering itself. If you can get good coverage of the surface of the pond then algae is starved out and the vascular (regular) plants do a good job of filtering the water.
Second, I highly recommend fish that are mobile enough to stir the water around and find all of the mosquitoes, but not so numerous as to overwhelm the planted capacity for filtration and oxygenation. I tend to like carp (such as goldfish and koi) which can breathe from the surface when they need to and pick at every little algae, snail, and weed invader that shows up in the water, but I expect there are many options.
Third, the amount of light you get will make a large difference in how happy your plants are and how much they bloom. My instinct tells me that half a day of Texas sun will be enough for most things, but your mileage may vary.
Leaves falling in the pond are detrimental unless you have a well cycled system with good oxygen levels and high filtration capacity (natural or otherwise). Cycled pond water is full of chemicals and bacteria which immediately set about degrading leaves that have fallen in, freeing the nutrients they contain. Again, mature, heavily planted tanks have less trouble with this.
I tend to run all of my small, outdoor ponds without electricity. This is heresy in some parts of the aquatic gardening world, so I don't advertise it loudly. I often temporarily run aeration in water imported from other ponds when setting up a new system, and circulation pumps in anything over 35 gallons. This means a combination of fountains (aeration and circulation), bubblers (aeration with localized circulation), and powerheads (underwater circulation only). I have a set of 100' 12 gauge extension cords for this temporary purpose, which I have been known to partially bury, with a box next to the pond to protect the connections. I'll keep these running for the first month or two as I'm planting and adding fish, and then back them off when nutrient levels drop and oxygenation levels remain stable. Keep fountain splashes 24" from water lily pads, though; they don't like it. I think it's possible, though harder to do without this step. You have to go very slow and careful with adding water, and if you move too fast and create anoxic conditions there is no fix but to aerate or drain the pool. I have also seen people successfully set up 25-35 gallon pools all at once without any electricity, but it doesn't work well for me in the long run unless I get the system properly cycled.
There is less of a safety net in the pond when it is smaller (less water to contaminate) or lacking external aeration and circulation. I am constantly assessing pond health:
smell--clean, not sulfurouscloudiness-absenttypes and locations of algae--harder to explain, but bodies of water go through cycles of different types which you can learn to recognizefloating and suspended particles--absent, as they get gooped up by healthy bacterial populations
I also keep test kits on hand for when I suspect something is wrong.
This pond, picture posted previously, is only ~150 gallons, two feet deep with very steep sides, and six feet across. It has had no electrical inputs in three years. It contains ~6 goldfish in the 4" range (hard to tell how big they are under the pads) and holds 4-6 medium or large hardy water lilies, a nuphar, and some water iris. It gets up to eight hours of sun/day and is in constant bloom from May to November, with anywhere from three to twelve blooms at a time. I need to split the water lilies and remove some of them. I've never fertilized them, though they are planted in pretty rich muck.
My tropical water lily ponds, which I can't get a good picture of since I'm in the process of tearing them up to move them, are run entirely differently. The fertilizer that I give the tropical water lilies puts a much heavier strain on the pond, but I keep elephant ears, thalia, cannas, and more in them to help with that. My tropicals are pulled out every year and I keep water hawthorne in the ponds which multiplies easily and blooms heavily and fragrantly in the cool air of early spring and late fall outside, and all winter long in the greenhouse. The greenhouse water lily ponds always run aeration, and often have underwater pumps and heaters when I want them to bloom nicely in the off season. Others here will have to fill you in on how they keep tropicals in zone 9a winter ponds if that's your interest.
This picture was of a newish pond, as you can tell from the material in the water and the poor surface coverage. At this stage I'm actively removing algae, but no longer using any electricity.
