This is an area where the answer now is already starting to be a lot different from the answers a few years ago, and where the conventional wisdom may not really be true anymore.
A few years ago, solar and batteries were crazy expensive per watt and watt/hour, and the only air conditioners that were available used massive amounts of power - it really wasn't at all feasible to have an off-grid camper that would have an air conditioning system. The standard advice was: if you need AC, you need shore power or a generator. Period.
However, things have changed pretty dramatically on two fronts. First, solar panels and lithium batteries have gotten way, way cheaper - you can now build a 400Ah battery bank with 800+ watts of solar for what a 200Ah system would have cost five years ago. Second, and maybe more importantly, DC-powered mini split air conditioners have recently hit the market at surprisingly affordable prices - you can get one for around $300-400.
These are the air conditioners you see on the roof of pretty much every RV. They're all-in-one units - everything is contained in the box on your roof, and they blow cold air down into your space.
1400W AC unit → ~1600W from batteries (with inverter losses)
= 133 amps/hour at 12V
On a 400Ah battery: ~1.5 hours runtime to 50% depth (3 hours to full discharge)
Even with 800W solar perfectly positioned, you're probably not breaking even.
These are the new kids on the block, and they work quite differently. A mini split system has two parts: an outdoor compressor/condenser unit (the part that gets hot) and an indoor air handler (the part that blows cold air). They're connected by refrigerant lines that you run through a small hole in your wall.
500W DC unit = 40-45 amps/hour at 12V
On a 400Ah battery: ~4-5 hours runtime to 50% depth (8-9 hours to full discharge)
With 800W solar in peak sun: generating 600W+ → nearly covers AC draw!
The term "mini split" refers to the system being split into two units - hence "split." The compressor (the power-hungry, heat-generating part) sits outside, and the air handler (the part that blows cold air) sits inside.
"Mini" just means it's a small system designed for a single room/zone, as opposed to a whole-house system. Perfect for a van!
The honest answer: it depends, but it's way more feasible than it used to be.
Then yes, a DC mini split can work for off-grid use!
Somewhere hot during the day but cool at night
Run AC during peak heat (when solar is also peaking), then turn it off at night and use your roof fan. This is actually pretty sustainable with a good solar setup.
Somewhere that's hot 24/7 (like desert summer)
You'll need a really big battery bank, or you'll need to supplement with shore power or a generator.
These are a bit more involved to install than traditional roof AC units:
Usually on the back doors or exterior wall
Usually on a wall or ceiling
Through your wall - needs proper sealing
Some units come pre-charged, others need professional charging
Electrical wiring is straightforward since it's DC
The installation isn't rocket science, but it's definitely more complex than just cutting a hole in your roof and bolting down a traditional AC unit.
I wouldn't prioritize AC in the budget. A good roof fan (Maxxfan), proper airflow, and strategic camping (seeking shade, higher elevations, cooler seasons) will get you pretty far. AC is expensive, uses a lot of power even with the DC units, and adds complexity.
If you're going to be in genuinely hot conditions regularly, or if you have health issues that require AC, or if you just really value being cool - the new DC mini splits have changed the game enough that it's worth considering.
It's no longer a "you must have shore power" situation.
You're not going to match home AC performance on battery power alone, but you can make a hot van bearable, which is a pretty big upgrade.
One more thing: These DC mini splits are still relatively new to the van world, so there isn't as much long-term data on reliability. You're taking a bit more risk than with established brands like Dometic. But at $300-400, even if you only get a couple seasons out of it, that's not the end of the world.