Extreme weather can lead to weather-induced disasters. These have a profound impact on communities worldwide, causing loss of life, damage to properties and infrastructure, and disruption of daily activities. In alignment with the United Nations Sustainable Development Goals, addressing the increasing frequency and severity of these events, exacerbated by climate change, is imperative. Exploring public perception and responses to weather disasters becomes crucial for policymakers to formulate effective strategies that not only mitigate the impacts but also contribute to the goal of ensuring sustainable and resilient communities. Social media, as a pervasive and real-time communication platform, has gathered a large amount of public opinion. In this work, we analyze public perception towards weather disasters based on tweets and metaphors. Metaphor, as a linguistic device, plays a pivotal role in unraveling cognitive processes and understanding how individuals perceive and make sense of concepts. We focus on tweets related to four distinct types of weather disasters i.e., floods, hurricanes, tornadoes, and wildfires, aiming to extract nuanced insights regarding public perceptions, concerns, and attitudes towards these specific events. We also deliver constructive recommendations, based on the insights.