I wouldn't start pulling anything yet. Oil can work its way out of the tranny and into the transfer case over time and high speeds, overflowing out of the t-case shifter and breather. That might not be the problem since this started when you got in the mud, but might be coincidental.


Another possibility is your t-case took on water somehow as been suggested and heat from driving caused it to overflow in the same manner.

Pull the t-case fill plug and see if a ton of oil comes out. That would be a good sign one of the above happened.

My advice would be to check the levels weekly if not daily, wash the whole area and see what happens.