question for you but what weather app / tool are you using in your personal life, as someone who works in that general industry.
I ask alexa and it generally does fine. If uncertain I go outside for a bit and look at clouds.
For the details, you just have to know how your local weather works - thunderstorms come in squall lines here, or are hot-day flash storms.
Blizzards follow warm still weather the same way, but mostly in Jan-Mar, when the jet stream curls away and will snap back to bring arctic air down.
Moisture (rain/slush potential) follows California rain by 2 days or so. If my friends in cali complain about rain, I know we're gonna have school closures if in the winter.
If I really need to drill in on rain/snow chance, I google for a weather radar and do prediction in my own head. (windy.com is ok, accuweather is real data to watch). Storms generally move linearly or rotate, and gentle rain is wide while torrential rain is clustered.
Locally, many of the old wives tales about the shape of clouds or direction of wind vs prevailing (with against, cross-grain) are true enough for 12h-24h predictions in upper midwest USA.