Having the doors on the Jeep can keep the mud out of the interior. Unless a) the puddle is deeper than expected and b) you hit it fast enough to splash the muddy water right over the windshield.
Fortunately all the electrical seemed to be working just fine on the drive home, so I think it was all on the surface. It did take me an hour to get it all cleaned and shined.
No more mudding without the top and doors on.