Actually leah_s clearly states in numerous posts that she doesn't refrigerate because she feels it dries the cakes out. I do not agree, but that is part of her reasoning for not doing it.
You do have to be careful when you refrigerate fondant cakes, because sometimes you will have condensation when you take them out, and as long as you know how to handle that correctly, it's not a problem.
When I lived in Las Vegas and decorated cakes as a hobby I never had an issue with condensation, after moving to Virginia I have had to adjust. I almost had a meltdown when I baked my first cake in the summer (VERY high humidity) and it had crazy condensation after one minute of being out of the refrigerator. I just let it sit, with a clean fan blowing at it (to avoid any kind of dust hitting the moist cake), and it dried fine- no spots. Now I know in the summer to make the cake refrigerator setting less cold (none of my icings are perishable), so it won't be such a drastic temperature change, but it will still be more firm for transporting than room temperature.