It's no the lack of a magnetic field that makes radiation from space dangerous nor the reason why it would be difficult to terraform Mars. A thick atmosphere protects us on Earth from space born radiation. Protection from a magnetic field depends upon polarity of the radiation. The atmosphere is far more effective. Also, if we wanted to warm up Mars, the desired temperature would dictate, via the Boltzmann distribution of temperature dependent molecular velocities, a situation where there would be a significant number of velocities greater than escape velocity for Mars, which has lower gravity than the Earth. If the Earth had the mass of Mars, we would have no atmosphere because we are much warmer. At least Mars can hold onto a tiny fraction of our atmosphere because it is so cold.