will sodium polyacrylate crystals + H2O mixed with ammonium nitrate make it colder? and if so 4 how long ?

Yes, but you may get some very chilly looks from the people trying to decide what you are planning to blow up with that ammonium nitrate.

You may not even need it. If water is able to evaporate from the moist gel, this alone could keep it quite cool. While ammonium nitrate will stop absorbing heat as soon as it is fully dissolved, a passive evaporative cooler can keep working for as long as it has more water than the air does.