Among parameter-efficient fine-tuning methods, freezing has emerged as a popular strategy for speeding up training, reducing catastrophic forgetting, and improving downstream performance. We investigate the impact of freezing the decoder in a multi-task setup comprising diverse natural language tasks, aiming to reduce deployment overhead and enhance portability to novel tasks. Our experiments, conducted by fine-tuning both individual and multi-task setups on the AlexaTM model, reveal that freezing decoders is highly effective for tasks with natural language outputs and mitigates catastrophic forgetting in multilingual tasks. However, we find that pairing frozen decoders with a larger model can effectively maintain or even enhance performance in structured and QA tasks, making it a viable strategy for a broader range of task types.