Idk where to post this but cake icing help!!

Okay so idk where I should’ve put this but I’m making my cake for my baby shower. The shower is Saturday, I was planning to do a cupcake cake , and bake the sup cakes Friday late afternoon / evening but idk when I should first do the icing. It won’t be small enough to fit in a cake box so I’ll be having to place the cupcakes in arrangement on a piece of thick cardboard covered in foil. My mom suggested icing everything Friday and putting the board with the cake in the fridge but idk. I won’t have a way to cover it all with the icing since it won’t fit on a standard cake board for a cake box and I’m worried the icing won’t be all that great if I do it the night before the shower party by putting it all in the fridge or even just leaving it out since it’ll be uncovered. Any suggestions???? I could really use some help. Anxiety is definitely kicking in 😩