Eowyn's "disguise" - who was fooled by it?

[symestreem]

I think it was the helmet that prevented Eowyn from being recognized. Tolkien calls it "the helm of her secrecy", and both Eomer and Imrahil recognized her with it off- so it's safe to say that anyone who saw her without her helmet would recognize her as a woman, and maybe Eowyn if they knew here. But knowing this, would she have taken her helmet off? Also, Dernhelm "never spoke to anyone".
I don't think anyone recognized Eowyn, because if they did they would have said something. They didn't know she could fight, and even if they did, it would technically be treason to not tell the king, since he had commanded she stay at Edoras.