Occasionally restrictions do apply, look at this map and click the WMAs you want to visit for information on them:
http://dwrapps.utah.gov/ram/start2
Seems like a few of them have a locked gate year round and you can't drive into them. Other than that, they're generally all closed to vehicles from December to May or January to April to give the animals a rest. Some have restrictions for certain areas within the WMA.
You can hunt any legal animal in them, and from what I can see they're all in the boundaries of some hunt or another.
Edit: Some WMAs are closed to the public for the winter and most of spring.