In recent years, deep-learning-based visual object tracking has obtained promising results. However, a drastic performance drop is observed when transferring a pre-trained model to changing weather conditions, such as hazy imaging scenarios, where the data distribution differs from that of a natural training set. This problem challenges the open-world practical applications of accurate target tracking. In principle, visual tracking performance relies on the discriminative degree of features between the target and its surroundings, rather than the image-level visual quality. To this end, we design a feature restoration transformer that adaptively enhances the representation capability of the extracted visual features for robust tracking in both natural and hazy scenarios. Specifically, a feature restoration transformer is constructed with dedicated self-attention hierarchies for the refinement of potentially contaminated deep feature maps. We endow the feature extraction process with a refinement mechanism typically for hazy imaging scenarios, establishing a tracking system that is robust against foggy videos. In essence, the feature restoration transformer is jointly trained with a Siamese tracking transformer. Intuitively, the supervision for learning discriminative and salient features is facilitated by the entire restoration tracking system. The experimental results obtained on hazy imaging scenarios demonstrate the merits and superiority of the proposed restoration tracking system, with complementary restoration power to image-level dehazing. In addition, consistent advantages of our design can be observed when generalised to different video attributes, demonstrating its capacity to deal with open-world scenarios.