Why is there a white powdery deposit in my swamp cooler?

That's just scale and mineral buildup. Evaporative coolers work by evaporating water; when they evaporate hard water that has minerals in it, the minerals stay behind. The better coolers have constant bleed lines or purge pumps to prevent this buildup by flushing it away. You can do it yourself by periodically draining all the water in the sump. Or you can install a bleed line or purge pump yourself.

But if you have one of the old coolers that uses thin aspen pads, know that you have to replace those pads at least every year. That type of older cooler requires a decent amount of maintenance; if you're not willing or able to do it, I would recommend replacing it with a newer unit that uses thick rigid media that lasts a long time instead of those aspen pads, and has a bleed line or purge pump to keep the scale buildup down.