Where do I store iced cupcakes over night??

I would store in an airtight container.  Cupcakes can dry out pretty quickly, especially if the whole top is not iced.

Just saw your other post.  You can leave out as long as your environment is not too hot.  Otherwise, throw them in the fridge.  If they are butter based, just make sure they come to room temp before serving.

Thank you :)

Will the buttercream get to soft if its in an air tight cupcake container?

I use smbc and have left them in an airtight container on the counter for several days (with the house probably around 70-75 degrees or so) and they were absolutely fine.  I would do the same with abc.

Just don't leave them near the stove or in the sun, haha!

:)