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 approaches have proven useful in tackling this problem. However, existing studies usually focus on training models for one specific task, location and variable, which are therefore limited in their generalizability and transferability. In this paper, we evaluate the efficacy of training deep learning downscaling models on multiple diverse climate datasets to learn more robust and transferable representations. We evaluate the effectiveness of architectures zero-shot transferability using CNNs, Fourier Neural Operators (FNOs), and vision Transformers (ViTs). We assess the spatial, variable, and product transferability of downscaling models experimentally, to understand the generalizability of these different architecture types.