It sounds to me as though this might be ripe for a Poisson Regression model where your dependent variable is number of accidents (you'd need to summarize your data by counting the number of accidents in each zip and for each weather condition -- I'm assuming the date/time is unimportant to you based on your post) and your independent variables are weather condition and zip (assuming you don't have too many zip codes or that you have enough data for the number of zip codes you want to model). This way, you can determine the effective increase in the average number of accidents for a given weather condition, averaged over all zip codes or for a given zip code. Assuming your data are uncorrelated you could use a regular Poisson regression model here, but depending on the circumstances of your study, independence might not be realistic, especially if you are talking about observations colliding with one another in a small area.
Of course, if you wanted to, you could always augment your existing data with weather data by merging based on zip code and date/time. This might allow you to model some additional weather phenomena at a more detailed level.