Whether or not a yule log needs to be refrigerated depends on the filling. If filled with mousse, it definitely needs to be refrigerated and not left out at room temperature for over 2 hours. Christmas is not the time to get food poisoning. But if your holiday cake is filled with buttercream frosting, it can stay out at room temperature. Cover with plastic wrap to prevent the cake from drying out. Refrigerating either version may help lengthen its shelf life, but make sure to bring it to room temperature before serving.