In the context of climate change and energy transition, the growing frequency of extreme weather events threatens the safety and stability of power systems. Given the limitations of existing research on load characteristic analysis and load forecasting during extreme weather events, this paper proposes a load-integrated forecasting model that accounts for extreme weather. First, an improved power load clustering method is proposed, combining Kernel PCA for nonlinear dimensionality reduction and an enhanced k-means algorithm, enabling both qualitative analysis and quantitative representation of load characteristics under extreme weather. Second, an optimal combination forecasting model is developed, integrating improved SVM and enhanced LSTM networks. Building upon the improved power load clustering algorithm, a load-integrated forecasting model considering extreme weather is established. Finally, based on the proposed load-integrated forecasting model, a time-series production simulation model considering extreme weather is constructed to quantitatively analyze the power and electricity balance risks of the system. Case studies demonstrate that the proposed integrated forecasting model can effectively analyze load characteristics under extreme weather and achieve more accurate load forecasting, which can provide guidance for the planning and operation of new power systems under extreme weather conditions.