A swamp cooler works fine to cool air assuming the incoming air has low humidity. But if your trying to cool the nutrient solution, you can't just pump nutrient solution through a swamp cooler without big problems. The problems being drastically changing the balance of the nutrient solution as some of the mineral salts deposit on the cooling pad. As well as the constant concentrating of nutrients/mineral salts as the water evaporates, both from the nutrients themselves as well as from the minerals in the water source. You can design it to cool the nutrient solution, but you have to keep the nutrient solution and swamp cooler water separate. I have a design to do it I call a reverse swamp cooler.
A typical swamp cooler is designed to cool air, but if you have ever built one or ran one you know the water gets cold, and you can use that cold water to cool the nutrient solution. The emphasis of the reverse swamp cooler design is on the cool water rather than maximizing air flow. That's why I call it a reverse swamp cooler. The revers swamp cooler is designed to maximize cooling pad space and surface area, while minimizing fan size (electricity use). You still want a good amount of cooling pad surface area to cool the water, but you don't need a lot of air flow like typical swamp coolers since the point is to cool the water, not getting a lot of cubic feet of cool air.
You need to keep the swamp cooler water and nutrient solution separate, but that's easy to do by running one through coils submerged in the other to get the heat transfer. The more cool water, the more heat (Btu's) it can absorb without changing temperature quickly. The air flow and cooling pad of the swamp cooler keeps circulating cold water to the coils. Cold moves towards heat, so the cold water pulls heat out of the coils, thus heat from the nutrient solution.