Devil's Garden CG at Arches will be closed from March 1 thru Oct 31, 2017. When we were last week the departing Campground Host comfirmed that there are not host scheduled for next season.
Watchman CG at Zion accepts (effectively requires) reservations year round - if you want a site with power.
All the other parks are first come, first serve. We were able to get into Fruita on Oct 29, but it filled by 5 pm. Arches NM and both CG at Canyonlands were filled by noon each day last week. We will try our luck at Lower Lehman Creek at Great Basin NP tonight, and North CG at Bryce Canyon on the 10th. So far temps have been acceptable - nothing below freezing yet.
We counted over 95 rigs parked in the BLM designated campgrounds around Moab - Kane Creek, Hwy 178, Sand Flats Road and Hwy 313. Kens Lake was full. Several folks with trailers/ pickup campers in the lower elevation Manti-LaSal NF campgrounds. BLM Sand Island at Bluff was full.
Personal note - we found dry camping at Goosenecks State Park an effective cheap alternative to Gouldings or the tribal CG at Monument Valley. We liked the Valley of the Gods BLM area much better than Monument Valley. Better views of the formations, much better road, and it didn't cost $20 (cash only) to get in for a drive thru.
Also don't miss the Moki Dugway (don't take a trailer or Class A/C over that road) and Muley Point.