This paper proposes a model for energy flexibility of cold climate air source heat pumps (ccASHPs) in both heating and cooling seasons. The proposed model ensures satisfying the customer comfort in terms of the desired temperature range while providing the energy flexibility as a function of the input power of ccASHPs. The proposed flexibility model is a linear programming problem, integrated into the home energy management system that maximizes the flexibility provision potential of ccASHPs by obtaining accurate models of ccASHPs’ power consumption, and heating and cooling capacity that are dependent on setpoint and indoor temperatures. The numerical results of implementing the proposed model in a sample house demonstrate the capability of the model in capturing the flexibility of ccASHPs without violating the comfortable temperature range of residents while lowering electricity consumption of heating and cooling by 7% and 11% in heating and cooling season, respectively.