A gas turbine system may include an exhaust gas processing system configured to process exhaust gas received from a gas turbine engine of the system. An exhaust path of the exhaust processing system is configured to flow the exhaust gas through the exhaust processing system. A tempering air system of the exhaust processing system is configured to introduce tempering air into the exhaust path to cool the exhaust gas. The tempering air system includes a tempering air pathway extending from an air inlet of the tempering air system to a tempering air outlet where tempering air is introduced from the tempering air system and into the exhaust path. A filter system of the tempering air system has a hydrophobic filter positioned along the tempering air pathway, the hydrophobic filter being configured to remove hygroscopic and deliquescent materials from the air flowing through the tempering air pathway.