OK. The reaction with ammonium nitrate dissolving in water absorbs some heat. That number is something we can calculate. I don't know the fo9rmula offhand, and I don't know the constants. But you can work on that.
You know water freezes at 0 C. (The numbers for constants will likely be in C, so get used to that now.) A solid block of ice won't react to get colder. But that's OK, as we dissolve ammonium nitrate and salt in the water, we lower its freezing point. Problem is, the more other thins we add, the more dilute this gets.
I don't think there's anything stopping a small amount of water and ammonium nitrate from getting quite cold indeed. You might even get enough to cover the bulb of a thermometer, and marvel at the very low temperatures. Of course, the smaller amount of water you have, the less ammonium nitrate you're dissolving. Dry ammonium nitrate doesn't get very cold on its own.
Here's how I'd cool a large amount of water. I'd use a different endothermic reaction. I'd add ice to water, and let the ice melt. With added salt and lots of melted ice, the solution can get quite cold indeed. The way the wold always does it cheaply and without complications.
A kid arrives every so often and wants to mix two chemicals and refrigerate an entire house, or something. I suspect that is what you're expecting too. That isn't possible. If it were, it would be commonplace in industry. You can try to calculate these things, or even try with a small amount of chemicals, but you seem instead to want an answer to an impossible problem, using the twin skills of "wanting it real bad", and "asking on a forum." I really doubt this plan is going to go anywhere.