Mexico has a very diverse climate, so part of the answer would depend on where you’re planning to go.
As far as Seasons, rains begin in May and end in November. That being said, your typical rainy day in much of Mexico begins clear and sunny with clouds gathering inthe afternoon and rain beginning at about 4 pm or just raining overnight. And both coasts are subject to hurricanes, peaking Aug-Oct.
A hurricane will likely cause rain inland as well as on the coast, and is more likely on the Caribbean and Gulf coast than the Pacific.
Though winters are generally mild, at altitude it can get cool. In the Mexico City suburb of Santa Fé they say 26 F / -4 F last week. I’ve very rarely seen snow in the City, but I’ve seen it and snow or ice can occur in the high mountains between Mexico City and Cuernavaca, for instance.
It can get blazing hot in some areas, and peak heat in the highlands is May (not as hot as lowlands), and July - September are often hottest in the lowlands.
These are generalizations, but you can narrow them down with the World Climate Charts offered
here. For example, see the charts below for Mexico City, and Hacienda Ylang, Veracruz. Temperatures are average daily highs and lows, not highest and lowest.