When extreme weather events occur, people often turn to social media platforms to share information, opinions and experiences. One of the topics commonly discussed is the role climate change may or may not have played in influencing an event. Here, we examine Twitter posts that mentioned climate change in the context of three high-magnitude extreme weather events – Hurricane Irene, Hurricane Sandy and Snowstorm Jonas – in order to assess how the framing of the topic and the attention paid to it can vary between events. We also examine the role that contextual factors can play in shaping climate change coverage on the platform. We find that criticism of climate change denial dominated during Irene, while political and ideological struggle frames dominated during Sandy. Discourse during Jonas was, in contrast, more divided between posts about the scientific links between climate change and the events, and posts contesting climate science in general. The focus on political and ideological struggle frames during Sandy reflects the event's occurrence at a time when the Occupy movement was active and the 2012 US Presidential Election was nearing. These factors, we suggest, could also contribute to climate change being a more prominent discussion point during Sandy than during Irene or Jonas. The Jonas frames, meanwhile, hint at lesser public understanding of how climate change may influence cold weather events when compared with tropical storms. Overall, our findings demonstrate how event characteristics and short-term socio-political context can play a critical role in determining the lenses through which climate change is viewed.