Wow. My first thought is, Gal invited you to go muddin' You may just want to ask her to marry you now.
Secondly "If" it's the other euphemism ... then you absolutely should ask her to marry you now. lol
But seriously - In any and all things (including things Jeep-centric) don't EVER do anything You aren't comfortable with.
Mud washes off. You will want to treat your Black plastic fenders etc if you have those. They do not love mud.
I'd spray the entire under carriage with a release-agent like fluid film, WD-40, etc so the mud washes off easier. A can or two is cheap and easy compared to hours with a high pressure washer.
Personally I'm not a fan of muddin' close second is rock crawling on purpose.
Just isn't my thing but I'm in the Pocono Mountains of N/E Pa.
I like trails, Beach (OBX) Farms w/streams and open old growth forest's etc.
To each their own.... but, yes on the pre-work in order to make clean-up easier and more thorough.
Have fun w/your new friend "dirty girl" if you marry her - forget I just said that