A gun was left outside over night. There was no dew or rain shouldn't the finger prints yet be on the gun? Or at least some of the prints since the trigger was pulled supposedly by the deceased

Why was the gun outside? Did the deceased kill himself outside? If so, why were the police not called right away? How did the gun end up being left outside overnight? Was the deceased also left outside overnight?

Yes, finger prints will remain... I'm fairly sure that even dew and rain would not remove the prints.

The fingerprints adhere to the gun metal because of body oils which are not soluble in water, so yes, they should remain (unless wiped off with a cloth).