Sherrie, I haven’t tried storing the whoopie pies at room temp, but I would be more worried about the cake drying out than the mousseline deteriorating if it is only a day or two. When I wrapped mine in plastic wrap, some of the crust stuck to the plastic when I unwrapped them (stored in the fridge). Like most butter cakes, these were the best within a day of baking.
I realize it would be safest to get Rose’s tested guidelines for keeping, but I do think it would be very similar to mousseline. Adding powdered sugar and butter to moussline probably won’t shorten keeping qualities. Perhaps a little label could be placed on the w. pie’s plastic wrap that says to freeze it if not eating soon?