The low-moisture, alkaline nature of bar soaps is its own preservative! I would think the humidity in the fridge owuld actually be a problem for storing soaps!
Even my rebatched cured CP soaps get better with age. I can only imagine that HP soaps do also. My rebatched CP soaps got richer lather and better conditioning. Don't ask me how or why. I can only say it did. One day I may be smart enough to know why, though.
I don't see any need to store your bars in the fridge. It's best to store in a cool, dry place. The only time I've ever had a problem is when my NaOH calculations were off, or if I didn't use distilled water. (From the bacteria in the water.) I love soap as it ages: it's like a fine wine.
I just tested a soap and took to market that has cured for a year. It is a watermelon soap made with watermelon juice and watermelon extract and it is a wonderful mild soap with tons of lather, no dos, even being made with 16% sunflower oil, and the fragrance actually held. Long curing does make a difference