Night flying will not significantly reduce radiation exposure (except for UV-A to your skin).
Cosmic radition (including some nasty high-energy stuff) comes from deep space and has nothing to with day/night.
Solar radiation is highly distributed by the earth's magnetic field but without going to the trouble to look up the relevant research I'd bet that you get more solar radiation when you have a direct line of sight to the source. But probably not orders of magnitude more.
You definitely get more UV-A during the day unless you wear sunblock (yes, I do).