Honestly, as someone who designed and installed our own off-grid system, if your coop is on the ground this is your best option:
https://www.backyardchickens.com/articles/alternate-method-to-prevent-water-freezing.73180/
Solar is possible, but heating requires a lot more power than you would think. A 200W heater run even just 8 hours a night t
is 1600W. If you buy 12V lithium batteries you'd probably want to go with a 200Ah battery to cover one single night. If you go any other chemistry of battery at all you'll need to double that for long-term battery health. For the sake of context, most of the year we manage our small off-grid home with the same sized battery - but we space heat with wood and water heat with LPG.
Conventional belief is that you should have battery capacity for at least 3 days because who knows what the weather is going to do. So 3x 200Ah lithium batteries or double that for AGM/Gel/lead acid batteries.
You'll obviously want the solar panels to charge the batteries. If you went with 1x 450W panel, that would take 3.5 hours of sun on a perfectly placed/angled solar panel to replace the amount of power you used overnight. That may do you if your weather is always good, always. If you ever go longer than a day without sun, or your coop is in a position where you can't get direct sun for that many hours, you'll have to scale up to 2 or 3 panels.
Because the usage is for a critical application, you'll need to consider whether you want a way to charge the batteries if the sun doesn't come out for a few days. For lithium it's ok to leave them largely discharged for awhile, for any other chemistry it's damaging to the battery and shortens their operating life, so you'll need to buy a generator and a battery charger.
Then you'll need to decide if the water heater will be AC or DC. Power comes from solar panels in DC, it's then inverted and fed into our homes as AC, then most of our appliances convert that back to DC in the appliance before use. You can save a reasonable amount of power in conversion losses if you do a direct DC system, but you have to either find a DC heating pad, or know if you can cut the plug off the heater you're looking at and wire it in directly. If you go DC -> AC -> DC for the ease of just plugging in your waterer you'll need to buy a good 500W or greater inverter because it's not good to run an inverter near it's maximum capacity for any period of time.
Any of the cheap ones you get on
Amazon will fail. Any of the cheap ones meant for people pimping out their trucks to go camping for the weekend will fail with consistent use. At this point I wouldn't go with anything less than Victron myself, but there are other reputable providers out there. If you ever can imagine using anything else on that power outlet, you'll need to upsize your inverter based on what load that might be.
Then, you'll want a grounding rod to ground your panel/s, inverter, charger, and generator to protect your investment. You will also want fuses after each major component. Then, of course, is all the wiring.
It's possible, and once you learn what you're doing it's pretty easy. It's also an expensive way to solve the problem, because heating something requires a lot of power. I'd be surprised if you wouldn't be significantly better off just buying a really grunty extension cord.
A quick wire size calculator tells me that for a 200W heater you can get by with a 12AWG extension cord that runs 200ft with acceptable voltage drop. The package will likely say 12/3 somewhere on it. So, like, two of these:
https://www.acehardware.com/departm...ords-and-power-strips/extension-cords/3014298
That honestly seems pretty grunty for just 200W, and another wire size calculator tells me 16AWG would do it which just feels more realistic, but you won't go wrong getting an extension cord that is gruntier than you need, so I'd still go with 12AWG myself.