LiDAR sensors are used in autonomous driving applications to accurately perceive the environment. However, they are affected by adverse weather conditions such as snow, fog, and rain. These everyday phenomena introduce unwanted noise into the measurements, severely degrading the performance of LiDAR-based perception systems. In this work, we propose a framework for improving the robustness of LiDAR-based 3D object detectors against road spray. Our approach uses a state-of-the-art adverse weather detection network to filter out spray from the LiDAR point cloud, which is then used as input for the object detector. In this way, the detected objects are less affected by the adverse weather in the scene, resulting in a more accurate perception of the environment. In addition to adverse weather filtering, we explore the use of radar targets to further filter false positive detections. Tests on real-world data show that our approach improves the robustness to road spray of several popular 3D object detectors.