Pinching antennas systems (PASSs) have recently been proposed as a novel flexible-antenna technology. These systems are implemented by attaching low-cost pinching elements to dielectric waveguides. As the direct link is bypassed through waveguides, PASSs can effectively compensate large-scale effects of the wireless channel. This work explores the potential gains of employing PASSs for over-the-air federated learning (OTA-FL). For a PASS-assisted server, we develop a low-complexity algorithmic approach, which jointly tunes the PASS parameters and schedules the mobile devices for minimal energy consumption in OTA-FL. We study the efficiency of the proposed design and compare it against the conventional OTA-FL setting with MIMO server. Numerical experiments demonstrate that using a single-waveguide PASS at the server within a moderately sized area, the required energy for model aggregation is drastically reduced as compared to the case with fully-digital MIMO server. This introduces PASS as a potential technology for energy-efficient distributed learning in next generations of wireless systems.