Is it not possible for them to just... spray it with ice cold water?
They are using a lot of water, as most as possible, from pipes at whatever temperature it is. There are no enough mobile refrigerators, not enough electricity to make them work, and it's very hard to transport cold water or ice if you don't use the pipes.
Also, the center of the tank is hot and reacting, but the external part is a nasty block if plastic that acts like a shield and isolate it from the cold water outside.
This is a common problems in big chemical plants when you have exothermic reactions. It's not enough to cold it down, you need to ensure all parts are cold down.
For comparison, there is a nice video by NileRed https://www.youtube.com/watch?v=phNLecfyWS8 He is making Bakelite that is a type of plastic. It's a tiny amount, in a lab, on purpose and he may make a few attempts. Anyway it overheat and instead of a nice piece of plastic he got a nasty block of foam with burned plastic. No imagine a huge tank of a similar chemistry reaction.
If they didn't have to worry about it imminently exploding I wonder if they could somehow wrap it with reinforcement (e.g., wrap some high strength metal around the tank to prevent it from deforming when drilled into) and then drill into it to extract the liquid?
One of my other less serious ideas was to helilift a Chernobyl style containment structure around it, but I imagine they don't have one of those just sitting around waiting to be used.
Chilling the water would massively complicate the logistics with a very marginal improvement in heat removal.
It is the same reason sweating cools the body much more effectively in low humidity than high humidity environments regardless of the temperature when you drink it. Attributing how drinking water cools the body via various effects is a classic introductory thermodynamics exercise.
So while I do agree that the evaporative cooling is probably doing most of the heavy lifting (in fact, necessarily so if the water temp ~= the tank's exterior temp), it's not unreasonable to suggest that using colder water would be more effective.
In fact, the wet bulb temperature there is apparently right around 16C, so they've basically cooled the outside of the tank as much as they can using evaporative cooling alone. They can certainly use it to _keep_ it there, but without something else they wouldn't be able to cool it further.
Presumably if there's an exothermic reaction happening internally then the core will continue to rise in temperature based on the temperature gradient through the material forming in the tank. I would assume (since my understanding is that it's some kind of plastic) that it has a fairly low thermal conductivity, so the core temperature will continue to rise as more of it turns to plastic even as the outside is cooled to the same ~16C.
In the limit if they were able to immerse it completely in very cold water (~0C) then the exterior of the tank would also be ~0C (supposing they were able to access sufficient quantities of water). I don't think that's practical of course, but again I don't think it's unreasonable to suggest that cold water would make a meaningful difference.
To put it differently, think through what it would take to refrigerate the volume of water that they are spraying. Can someone pull that together in a matter of minutes or hours?
I'm actually a little surprised that a quick search for "refrigerated liquid transport" didn't turn up anything. I would have sort of thought this was something that would exist (just because there are so many random things that are necessary for _some purpose_).
Well, "Ice Cold" water is ice and ice trucks are a thing - not to mention for fast substantive cooling 0 Celsius ice blocks on top of the tank would soak up far more heat energy than the same weight of 0 Celsius water.
As for the transportation of cold liquids, there are many LNG / Propane trucks about - pressurised containers for Liquefied Natural Gas.
Refrigerated liquid transport absolutely exists. Milk trucks is an example off the top of my head. Liquified natural gas is another.
That's not even funny:
1: Snowmaking equipment doesn't involve any chillers, they work by spraying a fine mist when the temperature is below freezing.
2: (Unless something changed in the last decade), the vast majority of snow in Tahoe is natural, not man-made.
3: There are closer ski areas than Tahoe. Mountain High, Mammoth...
4: Even if snowmaking involved chilling, (which it doesn't), it requires a significant amount of water and pressurized air, which requires specialized equipment and access to an energy source. It's assembled in the off season. Is it even practical to assemble all that in a matter of hours? Heck, is it even practical to disassemble it at a ski area's snowmaking equipment, truck it, and then re-assemble it?
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Lesson for you: Keep your assumptions in check. You keep coming up with very creative, but highly impractical, solutions.
If you're on an engineering team, bring your suggestions with a dose of humility, learn to listen, and see how more experienced people solve problems.
Furthermore, in a time-sensitive situation, constantly explaining to someone why their creative ideas are impractical takes precious time away from solving the real problem.