Adverse weather could potentially increase the probability of driving errors and hazardous driving actions and it is necessary to explicitly understand the endogenous and exogenous mechanism of how adverse weather-related determinants influence crash-injury severities and explore their spatiotemporal stability. To investigate the heterogeneity and spatiotemporal stability of adverse-weather-related crash severity determinants, this paper estimated two groups of random parameters multinomial logit models with heterogeneity in the means and variances. Crash data from Ohio and California were utilized between January 1, 2013 and December 31, 2016. Three crash injury severity categories were investigated including no injury, minor injury, and severe injury, in terms of multiple factors that could be categorized as roadway characteristics, environmental characteristics, crash characteristics, temporal characteristics, vehicle characteristics and driver characteristics significantly influencing adverse weather-related crash injury outcomes. Additionally, the temporal stability and space transferability of the models were investigated through a series of likelihood ratio tests. Marginal effects were also adopted to analyze the spatiotemporal stability of the explanatory variables. The findings exhibited an overall spatiotemporal instability while some indicators were also observed to be of relative spatial or temporal stability such as insurance, overturning, proceeding and early morning over the four-year period considered. This paper provided some immediate recommendations targeted at preventing crashes under adverse weather conditions across different regions and could potentially facilitate the development of crash injury mitigation policies. More regions could be considered to provide observations for spatial instability tests in future research.