What would happen to a woman astronaut who tried to walk on mars without a spacesuit or helmet?

It would be slightly worse than taking it off in space. The atmosphere on the surface of Mars is nearly a vacuum, so the astronaut would do well to notice the boiling saliva and tears and reseal the helmet immediately. Failing that, he or she would pass out in a few seconds, which is perhaps just as well. In space, you can only cool off by evaporation or by radiating infrared into space. On Mars, the tenuous air is just barely thick enough to conduct heat, and it's generally colder than northern Siberia in the January. So ... yeah. Don't do that.