The fusion of multimodal sensor data streams such as camera images and lidar point clouds plays an important role in the operation of autonomous vehicles (AVs). Robust perception across a range of adverse weather and lighting conditions is specifically required for AVs to be deployed widely. While multi-sensor fusion networks have been previously developed for perception in sunny and clear weather conditions, these methods show a significant degradation in performance under night-time and poor weather conditions. In this paper, we propose a simple yet effective technique called ContextualFusion to incorporate the domain knowledge about cameras and lidars behaving differently across lighting and weather variations into 3D object detection models. Specifically, we design a Gated Convolutional Fusion (GatedConv) approach for the fusion of sensor streams based on the operational context. To aid in our evaluation, we use the open-source simulator CARLA to create a multimodal adverse-condition dataset called AdverseOp3D to address the shortcomings of existing datasets being biased towards daytime and good-weather conditions. Our ContextualFusion approach yields an mAP improvement of 6.2% over state-of-the-art methods on our context-balanced synthetic dataset. Finally, our method enhances state-of-the-art 3D objection performance at night on the real-world NuScenes dataset with a significant mAP improvement of 11.7%.