Climate-related geohazards, such as landslides, floods, and coastal erosion due to climate change, are increasingly impacting human settlements and activities. This study, part of the European Project RESPONSe (Interreg Italy–Croatia), investigates the perception of climate change as a catalyst of future geohazards among the citizens of the Veneto region (northeastern Italy). A total of 1233 questionnaires were completed by adult citizens and analyzed by means of inferential statistics. The results highlight a widespread perception of climate change as a general threat for the environment, but not directly transposed to the frequency and intensity of future geohazards. Certainly, changes in temperatures and rainfall are widely expected and acknowledged, yet the comprehension related to the hydrogeological effects seems to vary proportionally to the physical proximity to these hazards. Such outcomes underline that there is still a common lack of understanding of the eventual local impact of the climate crisis. For these reasons, it is suggested that decision makers consider directing their efforts to enhance the citizens’ knowledge base in order to build a climate-resilient society.