Doable but expensive. Your better off buying a portable/fixed solar powered evaporative cooling unit.
It would be fairly easy and reasonable money wise, to run the A/C fan off of solar.
You could run other items off of solar, like lights, etc.
But the best overall solution is to install a grid tied system. You can start as small as you want(or what the power company dictates) and then add on. It's expensive to generate your total need. For my house where I live the system is over $55,000.00. But you can offset it.
A grid tied system generates power for the electrical company and that power goes into the electrical grid. The power company installs a new meter, if necessary that spins in both directions. So, if your system is producing more power than you are using, the meter spins backwards. Should you generate a surplus of power your bills will show a credit and/or the power company will pay you a rate per kilowatt hour of power.
Along with your grid tied system and transfer switch to disconnect you from the grid, you can also install a battery bank. The system can keep your batteries charged and send power to the grid. When the power goes out, you can disconnect from the grid and use your batteries to keep essential items running(refrigerator, lights, a well pump for water, etc)
For backup power you'd probably be better off with a generator system. But for small outages, batteries could get you buy.
Solar power can be affordable. If you are a do-it yourselfer you can make an inexpensive system for $300 or less that you can run a light, fan, laptop, etc off of. You could most likely power your most used room for a reasonable amount of $$.