Rohan did not light the signal beacons to alert Gondor of danger, nor did it send any messengers. When the Westfold fell, Théoden was under Saruman's control , so he would not have requested aid ...

Anyway, I was thinking about the part where Gondor sends a signal to Rohan asking them for military aid. Since this was before the invention of email, they had to do it with a signal fire.