Historical archives on weather events are collections of enduring primary source records that offer rich, untapped narratives of how societies have experienced and responded to extreme weather events. These qualitative accounts provide insights into societal vulnerability and resilience that are largely absent from meteorological records, making them valuable for climate scientists to understand societal responses. However, their vast scale, noisy digitized quality, and archaic language make it difficult to transform them into structured knowledge for climate research. To address this challenge, we introduce WeatherArchive-Bench, the first benchmark for evaluating retrieval-augmented generation (RAG) systems on historical weather archives. WeatherArchive-Bench comprises two tasks: WeatherArchive-Retrieval, which measures a system's ability to locate historically relevant passages from over one million archival news segments, and WeatherArchive-Assessment, which evaluates whether Large Language Models (LLMs) can classify societal vulnerability and resilience indicators from extreme weather narratives. Extensive experiments across sparse, dense, and re-ranking retrievers, as well as a diverse set of LLMs, reveal that dense retrievers often fail on historical terminology, while LLMs frequently misinterpret vulnerability and resilience concepts. These findings highlight key limitations in reasoning about complex societal indicators and provide insights for designing more robust climate-focused RAG systems from archival contexts. The constructed dataset and evaluation framework are publicly available at https://anonymous.4open.science/r/WeatherArchive-Bench/.