Climate downscaling, the process of generating high-resolution climate data from low-resolution simulations, is essential for understanding and adapting to climate change at regional and local scales. Deep learning has shown great performance in this task. However, existing studies primarily focus on training models on a single dataset, which limits their generalizability and transferability. In this paper, we evaluate the approach of pretraining deep learning models on multiple diverse climate datasets to learn more robust and transferable representations. We evaluate the effectiveness of pretraining using CNNs, Fourier Neural Operators (FNOs), and a CNN-ViT model. Through empirical experiments, we assess the spatial, variable, and product transferability of the pre-trained models to understand their generalizability. We also explore the use of fine-tuning on the pre-trained models to further improve the performance. Our results demonstrate that the proposed pretraining approach significantly improves climate downscaling performance in most scenarios.