Afterwards, you should check the following:
- Engine Oil
- Tranmission Fluid
- Transfer Case Fluid
- Axles
- Air Filter
- Greasable joints
- Maybe coolant as well
Now contamination of any of these is easy to spot. It will be milky. Engine oil I haven't seen, but I have seen t-case/transmission fluid that's been contaminated... Transmission fluid will look like strawberry chocolate milk, and I've seen BLACK atf come out of a t-case...
Axle-lube will be milky, it doesn't look right. I assume oil will look the same.
What happens if you don't change it out if it's contaminated? The water in the fluid will boil as it heats... Steam does nasty things, especially to automatic transmissions. If you don't change contaminated tranny fluid, you'll end up buying a new transmission...
The air filter may have gotten wet, and if so you may want to replace it (or wash it if a K&N).
As for what to do before going into deep mud/water, it handles it fairly well stock.
Some people coat up all the connections with di-electric grease to keep the water out, and you may want to grease every zerk fittings you can find (before and after).
That's about all I can think of...
Oh yeah, roll up the windows and turn off the A/C...

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If you have a permanently spinning plastic (flex) or metal fan, then replace it with a clutch-type or an electric fan. That way the fan won't pull itself into the radiator when it grabs the water. But you're pretty good with the Ram's fan.