I am powering my whole house 100% off grid with 10kw of panels and inverters and a 3000lb pile of deep cycle lead acid batteries. So i can confidently say, yes powering a shipping container from solar/inverter/battery will be very easy and even fairly cheap. You could potentially piece together a minimalist setup that would do that stuff for under $300 (highly dependent on how much battery you want), and by the time you hit $1000 you could even include a $150 ac window unit in the $1000 and sit in front of it taking a break when the sun was good. Seriously! Go for it!
Edit: I should elaborate i suppose.. the key is mostly in USED solar panels. A used solar panel that isn't broken is basically 95-99% as good as new and depending on how old it is it might be 1/10th the cost of new. I bought my 240w panels for ~$36/ea. The battery in the setup only needs to be large if you intend to actually power things overnight. The block heater overnight is a lot more expensive to build around, than a circular saw that's only used when the sun is up. During the day the battery will mostly serve to give brief surges of power during motor starts for your saws etc, but if you have at least several hundred watts of panels (which is possible to do for $100 depending on your patience watching the local facebook marketplace, craigslist etc) it will not do much else and thus doesn't need to be very big at all.. UNLESS you want to power a bunch of stuff overnight. Lights barely count. If they are LED you can light up a half acre with a car battery overnight. But electric heating elements could be a big deal depending on how big they are. If you're talking about a 40w heater running for 8hours a night, that's 320 watt-hours and again even a car battery could comfortably do that. If you're talking about a heater way over 100w, and ive seen some coolant heaters up to 1500w, then you are getting into buying a bunch of battery to support that and it will get expensive quick. If you give up on the block heater idea this goes right back to being cheap.
Somewhat unrelated and a little pie in the sky: My old 2009 Prius had a coolant 'thermos'. It was a highly insulated canister that stored hot coolant, and when you started the engine cold it would release that hot coolant into the system and heat the engine much quicker. It could keep coolant hot for 3 days. A diesel would need to be heated BEFORE it started, but still thought that was a cool anecdote..
I bought my 20' container for $1600 and i WISH they were still that cheap. I'd buy more.