As anthropogenic climate change progresses, there is an increasing need for individuals to make appropriate decisions regarding their approach to extreme weather events. Natural hazards are involuntary risk environments (e.g., flooded roads); interaction with them cannot be avoided (i.e., a decision must be made about how to engage). While the psychological and sociocultural predictors of engagement with voluntary risks (i.e., risk situations that are sought out) are well-documented, less is known about the factors that predict engagement with involuntary risk environments. This exploratory study assessed whether mental health (depression, anxiety, and stress symptoms), personality traits, and cultural worldviews combine to predict engagement with involuntary risk, using the situation of floodwater driving. An Australian sample (N = 235) was assessed via questionnaire and scenario measures. Results were analyzed in a binomial logistic regression assessing which individual factors predicted decision-making in a proxy floodwater driving scenario. Agreeableness and gender were individually significant predictors of floodwater driving intention, and four factors (named “affect,” “progressiveness,” “insightfulness,” and “purposefulness”) were derived from an exploratory factor analysis using the variables of interest, though only two (“progressiveness” and “insightfulness”) predicted floodwater driving intention in an exploratory binomial logistic regression. The findings highlight the need for further research into the differences between voluntary and involuntary risk. The implication of cultural worldviews and personality traits in interaction with mental health indicators on risk situations is discussed.