Thermoelectric energy conversion based on flexible materials has great potential for applications in the fields of low-power heat harvesting and solid-state cooling. Here, we show that three-dimensional networks of interconnected ferromagnetic metal nanowires embedded in a polymer film are effective flexible materials as active Peltier coolers. Thermocouples based on Co-Fe nanowires exhibit much higher power factors and thermal conductivities near room temperature than other existing flexible thermoelectric systems, with a power factor for Co-Fe nanowire-based thermocouples of about 4.7 mW/K2m at room temperature. The effective thermal conductance of our device can be strongly and rapidly increased by active Peltier-induced heat flow, especially for small temperature differences. Our investigation represents a significant advance in the fabrication of lightweight flexible thermoelectric devices, and it offers great potential for the dynamic thermal management of hot spots on complex surfaces.