This paper rethinks image histogram matching (HM) and proposes a differentiable and parametric HM preprocessing for a downstream classifier. Convolutional neural networks have demonstrated remarkable achievements in classification tasks. However, they often exhibit degraded performance on low-contrast images captured under adverse weather conditions. To maintain classifier performance under low-contrast images, histogram equalization (HE) is commonly used. HE is a special case of HM using a uniform distribution as a target pixel value distribution. In this paper, we focus on the shape of the target pixel value distribution. Compared to a uniform distribution, a single, well-designed distribution could have potential to improve the performance of the downstream classifier across various adverse weather conditions. Based on this hypothesis, we propose a differentiable and parametric HM that optimizes the target distribution using the loss function of the downstream classifier. This method addresses pixel value imbalances by transforming input images with arbitrary distributions into a target distribution optimized for the classifier. Our HM is trained on only normal weather images using the classifier. Experimental results show that a classifier trained with our proposed HM outperforms conventional preprocessing methods under adverse weather conditions.