I live in an area like that as well, and the station broadcasts the same info you see on road signs and web sites. If the lights are flashing it's usually playing "snow tires advised for vehicles..." on loop.
the kind of situations people describe where car AM radio is essential feel like corner cases that involve lack of planning and poor judgment or really bad luck. No cell service, no portable radio in your travel kit, no way to stop and ask anyone, and you can't just turn around when you see a flashing sign? It sounds like the plot of a horror movie.