You know it...
Which section are you referring to?
You used to be able to travel along the Muddy Creek from the Hidden Splendor Mine to the Muddy Creek river ford north of Factory Butte. It was closed several years ago, 02'ish. This is the location the disable veteran did the protest ride 2 years ago now? Would be a neat section to drive, could get a bit sketchy with a lot of water. There are some trip reports floating around the web of those that ran it prior to closure, in one case they had to get a tow truck out of Green River to rescue them
You can still cross the Muddy Creek between Factory Butte and the Little Wild Horse Mesa, it can get nasty and borderline impassible:
You also used to be able to cross the Muddy Creek at the Tomsich Butte Mine, it crossed over and lead on what I believe are some old mine roads on the west side of the river. That was closed several years ago.
You can also still cross it at the Lone Tree Crossing, nothing major there, its out in the flats and scenic in its own right, worth the drive if you happen to find yourself in the area.
Here is the Muddy Creek crossing north of Factory Butte in the fall of 07', just weeks before the water was running 3-4' deep in spots. We had to drop down the ledges and fight the muddy river bottom through the tamerisk. Richard and I came through there a couple of months ago and it was no problem at all.