If they had liquid nitrogen to dump on the exposed spent nuclear fuel, would that be a good thing.
One problem is the temperature (so cold that it would be dangerous for the workers -- could only be done with special equipment remotely controlled).
But unlike liquid hydrogen or liquid oxygen, it would not blow up and even if there is some sort of nuclear bombardment to change into other elements, it would not be dangerous (except for radioactive isotopes).
Getting Liquid Nitrogen there would be one problem (with enough volume). Having special equipment to spray such cold material is another (uncharted ground).
Dry Ice is another possibility, but since it is composed of oxygen (very combustible) and carbon (another fire hazard), if there is a chemical reaction it could be bad...
The ability of liquid nitrogen remove heat is about 1000 times less that that of water per unit of mass. Also the flashing away of gaseous nitrogen would carry with it large and concentrated amounts of radioactive particles. Dry ice is capable of removing about 100 times less heat than water per unit of mass. Handling large quantities of solids is very much more difficult that the same mass of liquids. The oxygen in carbon dioxide is not available to support combustion as you suggest in your subsequent post.
Yes, LN2 would be a good thing.
But if they can’t pump in H20, how do you think they could manage LN2?
Inside all these buildings there is total darkness (no windows, for obvious reasons). Workers move around with flashlights or headlamps. This is what happens in a “station blackout”.
Via NHK, the heroic workers have tried to supply water using “manual pumps”. Our old farm pumps—manual—could not ever supply 1 million gallons.