I'm still wearing my winter coat in the spring because New York is rather chilly. Nights still feel cold. I think you're fine until the temperature gets way warmer and it's less breezy out. I'd rather being over dressed (be able to relieve myself of clothing) rather than to be under dressed (where I am standing outside shivering).
Do you really even need a jacket during Spring? And if you live in the US, then it should be easy to find something extremely cheat. If you don't want to though, then you will get some weird looks, but who cares?