By "chaotic weather," we're referring to weather in general, rather than some specific events. Weather is always chaotic, because it can change very quickly and, at more than 7 or so days, unpredictably. Sometimes, these changes can be so large that they can affect the overall seasonal average. Regarding your second question--we don't currently have many forecasts for how variable the weather within a season is, but (in my opinion!) there is some potential for this, because climate signals like ENSO also affect daily variability.