Self-sustaining off-grid energy systems may require both short-term and seasonal energy storage for year-around operation, especially in northern climates where the intermittency in both solar irradiation and energy consumption throughout the year is extreme. This paper examines the technical feasibility of an off-grid energy system with short-term battery storage and seasonal hydrogen storage, comprising a water electrolyzer and a fuel cell. The study is based on data from a currently grid-connected residential single-family house in Finland with an existing 21 kWp photovoltaic (PV) installation and a ground source heat pump based heating system. Energy system performance is simulated using real PV power generation data as well as data on grid electricity import and export from the house over a three-year period to find the minimum combination of battery and hydrogen storage system capacities capable of year-round off-grid operation. It is concluded that technically feasible solutions are available for the proposed setup. The most significant factor affecting the system dimensioning is found to be high peak electric power demand during times of low PV power generation, indicating a need for smart power control. Demand for battery storage capacity is found to be significant only to about 20 kWh. Fuel cell and electrolyzer nominal powers of at least 4 kW and 5 kW to 7 kW, respectively, were found to be sufficient for off-grid operation with the studied system. The storage capacity demand for 170-190 kg of hydrogen annually is, however, impractically large for residential houses.