Drying it out is fine, but may do no long term good unless you dunk that sucker in distilled water. Really.
Distilled water is an insulator (doesn't conduct electricity). Rain water, on the other hand, due to all the contaminants it picks up from the air, including sulfur dioxide, is not and will conduct electricity shorting things and worse.
From the web, "Sulfur dioxide, SO2, is a colorless gas or liquid with a strong, choking odor. ... Sulfur dioxide dissolves easily in water to form sulfuric acid. Sulfuric acid is a major component of acid rain. Acid rain can damage forests and crops, change the acidity of soils, and make lakes and streams acidic and unsuitable for fish." Oh, and drones.
If you don't flush the drone with distilled water, the rain water will dry, leaving behind all the dissolved contaminants on the metallic portions of your drone (think connectors and circuit board traces etc). Humidity in the air will suffice to cause continuing electrolysis and galvanic corrosion.
I would first rinse thoroughly in fresh clean tap water - this should remove most of the bad stuff. Follow that with distilled water. Then shake to remove as much water as possible. Use a fan to direct air onto the front of the drone (air inlets). A warm air outlet from a heater is good (don't overheat). Time is your ally, don't power up until it is completely dry. Desiccant, silica gel, works a better than dry rice.