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The present paper introduces the time between the start of a snowfall and the occurrence of a motor vehicle accident as a novel measure for evaluating motor vehicle safety during snowfalls. Detailed information of accidents that occurred during snowfalls between 2017 and 2020 in the state of New York are used to explore the accelerating or delaying effect of different factors on the time between the start of a snowfall and the occurrence of an accident. To that end, the hazard-based duration modeling framework is employed, and to account for multiple layers of unobserved heterogeneity, a random parameters with heterogeneity in means and variances approach is introduced – for this first time, to the authors’ knowledge. The temporal stability of the factors across the study period is investigated through conducting a series of systematic likelihood ratio tests, and the factors are not found to be temporally stable …