Hi everyone! I always store my cupcakes in cardboard cupcake boxes. ( like cake boxes but they have inserts for the cupcakes to sit ) I never have an issue with sweating and it's very humid in Australia! I also never refrigerate them either. I've never had them drying out. I experimented one day with a few cupcakes to see how long they would last! After the third day, they were still nice and soft! I would of let it go longer but I don't keep anything out for more than that time! The cardboard absorbs the moisture and everything stays perfect.
I'm going to try this method. I have 50 cupcakes to make for a party this Saturday. I plan to bake the cupcakes later on today, let them completely cool, then store them in a half sheet box with parchment on both the bottom and resting on top. I'll cover them with the box lid and leave them on the counter. If they look like they're sweating, I'll prop open the cover a bit to let the air circulate (my mom used to do this with Tupperware, btw). I'll be icing/decorating them Friday night as the party at noontime Saturday and I won't have time to do them in the morning.