So, yes, I do wear the same coats/ jackets in spring and fall, but with exceptions. Summer is a separate category.
Like Angie, on the cold spring days like yesterday/ today, I am wearing my winter coats! I'll wear my lilac wool in cold spring (March) or my long blue wool coat or one of the light puffers.
On cold fall days, I'd be more likely to reach for the blue or reds.
As things warm up into true but still cool-ish spring, my choices are: leather trench, leather moto, or sweaters with a raincoat over top.
Once it's warmer, as well as for summer AC or cooler days/evenings, it is denim jacket or linen jacket or a light tweed jacket. The raincoat is oversized so can go over these if required.