I'm with amanda. If you're worried about it being too dry, you can drizzle it with a sugar syrup before frosting. (1 cup syurp = 6 T sugar brought to a rolling boil with 2/3 cup water while stirring. Remove from heat then cover and cool to room temperature. Add 3 T liqueur, and enough water to bring it to a cup volume.)

Either is fine, but I prefer to let the cake cool completely, and wrap it in plastic wrap until serving. If you decide to go the fridge route, just make sure you take it out early enough for it to come to room temperature before serving.