A section of the Mist Trail from the John Muir Trail junction (just uphill from the Vernal Fall footbridge) to the top of Vernal Fall will be closed Mondays through Fridays from September 7th to November 4th between the hours of 6:30 am and 4:00 pm. I think Half Dome hikers will be able to use the Mist Trail since they usually set out by 5:30 or so.
The trail should remain open on weekends.
It is possible that the trail will be closed overnight once in awhile - check the gate. Here is a picture of the gate
Here is a (winter) trail map. The part of the Mist Trail that will be closed weekdays in Sept, Oct, & Nov is the the red "Trail Closed" close to the river. The other red "trail closed" that is left (uphill) of Clark Point is open; that's the John Muir Trail. This is just the best map I could find; sorry it's not entirely accurate.