Passive variable insulation (PVI) could reduce the energy consumption for heating and cooling of buildings compared to traditional static insulation without requiring active control and sensing. However, existing PVI systems are limited to single-season operation. Here, we demonstrate a PVI thermal circuit consisting of two anti-parallel oscillating thermomagnetic diodes that enables passive heating during a warm winter day and passive cooling during a cold summer night. Centimeter-scale prototype experiments show that the PVI has a narrow 4oC temperature regulation band, functions in all gravitational orientations, is durable over >104 oscillation cycles, and has a circuit-level passive thermal switch ratio of 3 under ambient conditions. Thermal modeling over the US climate zones shows that PVI can reduce undesirable building envelope heat flows by up to 47% for base-case parameters, motivating further study of passive variable thermal insulation strategies for the building envelope.