As a member of a crazy 4x4 club,with scuba divers as members we had a lot of drowned motors as a result of deep water crossings.
We always stopped and let the engines cool before crossing lakes and rivers and kept revs low to avoid cracking a head if the motor sucked water.
In all cases of water intake into a cold low reving motor no permanent damage was done (we acted immediately).
After pulling the oil drain plug, allowing the pure water to drain, then letting a bit of the malted milkshake to drain, add some fresh oil, pull the plugs (or injectors for the diesels) crank, (avoid the bullet like jets of water from the plug holes), wire dryer and quick start (ether), then watch the steam from your exhaust until full oil change.
Did that with 2 of my own off road trucks, and helped many others do the same.
We had hose snorkels on our diffs, trannies, and transfer cases so all oils in the car should be changed as those areas could have sucked water past pinion seals etc. if the car was hot.
CERBERUS