Trying to do a backpack trip out of the Badger Pass area can be frustrating at this time of year, and it depends on snow. If there is a sufficient snow depth, then the Badger Pass Ski Area will be open, the parking lot will be plowed, and the Glacier Point Road will be plowed only that far. If there is insufficient snow depth, then the Badger Pass Ski area will not be open, and the parking lot is unlikely to be plowed (because it isn't necessary). Sometimes the problem lies in the road. Sometimes it is slick enough that NPS has it closed and gated, but yet there isn't enough snow. You get into a situation where you really can't get up there to the trailhead, so it is important to have some alternatives up your sleeve. One weird alternative is to park at Chinquapin and hike _up_ the Chinquapin Run, which brings you up to the backside of the Badger Pass beginner slope.
Incidentally, that bottom stretch of the Glacier Point Road routinely has the infamous R3 rating during winter. That means chains on every vehicle, even 4WD.
I've seen people plan a trip to go up the Glacier Point Four Mile Trail, and then they discovered that NPS had closed it because of danger.
An easy alternative is to park near Crane Flat and go up to the Crane Fire Lookout. It is a little exposed for weather, but the view is good and the distance is short.