Never done it in a HMMWV: a lot of the trail is pretty easy. If you go it clockwise you really dont even need 4x4. If you do it counterclockwise low-range is helpful on some of the steeper climbs. May be a few spots that the Tamarisk will leave pinstripes, but nothing crazy!
Just remember to get the permit. They have trail cameras and ticket if you cross into Canyonlands without a 4x4 (even just for a picture) without it. They have even started to ticket AWD rigs that attempt it. My van was a factory AWD, that I added a true 4x4 transfer case to and it was a fight to prove it was now a 4x4........
