Previous contributors pointed out interesting ideas about the range of possibilities for choice of anlytics. But, I think there is a major difference whether we are looking at this question as a predictive experiment or as an observational analysis. If we do the former, we may be able to test hypothesis about the causal relationship between whether and spending. But, if we look at the data retrospetively, we can only talk about it in terms of possible correlations, which may or may not be causal.
I think a meaningful research into the impact of wearther on consumer spending needs designing an experiment in one geographic locations to minimize the impact of socioeconomic factors. Daily or time-interval data can be collected over few years, for certain weather related factors such as rain, cloud, excessive cold, wind etc, And, as other contributors pointed out, for various types of products (essential, non-essential, etc.). Regression analytics should be used to define causal relationship between these weather parameters and spending in each category.
If the study is retrospective, then I would also think of limiting the study in one geographic location to minimze the complicating impact of the wide range of socioeconomic contributing factors, such as income, weather differneces, social habits, etc.