The most dangerous radiation events in space are due to solar flares and coronal mass ejections - solar proton events (SPEs). If you are caught outside in just your spacesuit or a lightly shielded vehicle during a major SPE, the dose of ionizing radiation (high-energy protons) could be enough to kill you if you stayed outside, oblivious to the danger, for several hours. SPEs don't happen that often, and when they do, you will have a few minutes warning that they are coming that could allow you to get to shelter in time to avoid the really dangerous ionizing radiation. The x-ray and gamma rays from the event will arrive at light speed and give advance warning of the wave of high-energy protons on its way. Astronauts working outside on a planet would likely try to always remain within reach of a shelter that can shield them from the ionizing radiation when alerted by heightened x-ray and gamma radiation of a SPE on its way. The x-rays and gamma rays aren't good but aren't that dangerous.
If you went out at night you would avoid the risk of SPEs altogether. But the ionizing radiation in interplanetary space is mostly GCRs - galactic cosmic rays. When the sun is more active, during solar maximums or briefly during SPEs, the amount of cosmic radiation is reduced, but it is always a concern. The cosmic radiation dose in interplanetary space has been assessed by the ACE probe as being about 0.4 Sv/year during the solar minimum of the sun's 11 year solar cycle, and 0.9 Sv/year during solar maximum. On any planet surface, half of that will be blocked out by the mass of the planet under your feet, making the dose 0.2 Sv/year to 0.45 Sv/year - if you were outside all the time. Shall we say for the sake of argument astronauts could be outside up to a quarter of the time? That would be 0.05 to 0.1 Sv/year, roughly. Whether you are out during the day or night makes no real difference to this dose, night work would just prevent the risk of being out of reach of adequate shelter in the event of an SPE.
0.1 Sv is associated with a slightly heightened risk of cancer. Crew on the ISS receive doses of 0.08 Sv over the course of their 6 month stays during solar maximums. Ionizing radiation is considered the cause of an increased incidence of cataracts among astronauts. Other than that, it is not clear what health risk this level of cosmic radiation exposure represents. If you lived on an off-world base it would be something to keep in mind as the decades wore on, maybe, but your main defense would to always be close enough to adequate shelter to avoid SPEs, and ensure you would be notified of their approach. If you do that, whether you are out in the day or the night makes no real difference.
