I heard they wore normal clothes, so that they could blend in better, and that the black suit comes from Japanese theatre - it would make a scene depicting an assassination seem more like it really did come out of nowhere.
hi! check out this very detailed post from the FAQ on Ninja by /u/asiaexpert, which includes these comment
For example, they did NOT wear completely black tight fitting body suits. When they were in regular samurai gear ( the gear they normally wore, as they really were samurai), they often wore lighter and plain kimono.
They would wear monk outfits or disguise as beggars while traveling or escaping to avoid detection. Other times they would pretend to be traveling performers and actually attract as much attention as possible on purpose, in a sort of reverse-psychology. The idea is that a samurai would never fall to such lows so they would never imagine in a million years that the smelly hobo monk is actually carefully gauging their military strength.