Before you put the cooler away take a ball of paper towels and put a little artificial vanilla on the paper towels. Throw them in the cooler and the cooler will smell good as new next time you pull it out. I keep a roll of paper towels and a bottle of cheap artificial vanilla on the shelf right next to the coolers. Alot of times when I am getting the coolers ready I will just put the paper towels I pulled out of the cooler on the work bench and re-use them when I get home.
The paper towels also soak up that little bit of moisture left over after you wash it out.
No more musty smelling coolers