Is radiation nearly as much of a problem outside the orbit of
say, Mars as it is closer to the Earth? I'm wondering if deep space
vehicles have more or less need for protection from radiation than those
that are exploring nearer to the Sun.
I wouldn't say less. Eventually you get out into interstellar space and there things would be fairly constant. The effect there would be minimal. They would stay minimal until you approached a stellar system of
Although some researchers have suggested that it would be better to go to Mars during a period of solar maximum when the sun is producing the most radiation, because then the sun has the strongest magnetic field which shields the solar system from very high energy galactic cosmic rays which would be impossible to shield against on your spaceship.