I didn't taste my cupcakes before frosting them. I tasted one and it is dry. Will putting them in the fridge moisten them or dry them out?

This is not related to the problem, but if you slice the cake part of the cupcake horizontally in half, and put the bottom half on top of the icing, you get a "sandwich" with icing in the middle, making for a more satisfying way to eat the cupcake.

yes, the fridge will dry them out. brushing on simple syrup (sugar + water, in equal measures and heated until the sugar dissolved + flavoring of choice) might give them an assist. I don't think i would inject the syrup directly into the cakes though.

No, putting them into the fridge will not moisten them and it would probably dry them out even more.

You could try to inject a syrup, but it's might now be moist like you want (i.e. more on the wet than moist).