Borek already gave hints about the temperature drop...
The amount of absorbed heat increases like the amount of substances. If the substances, ammonium nitrate and water, cool only themselves, the absorbed heat cools a quantity of matter that increases equally, so the temperature drop remains the same.
But if you use the reaction to cool the same amount of target material, say a bottle of champagne, then a lower amount of absorbed heat from the same target amount produces a smaller temperature drop.