Normally Camp 4 is the winter backpacker's campground, but since it's closed due to COVID-19, the only alternative is the Hetch Hetchy's backpacker's campground--although I'd call a ranger to make sure you can camp there for a non-Hetch Hetchy trailhead if that's the case. Normally dispersed camping outside the park would be an option, but is currently not allowed in any of the adjacent national forests. Note that Hetch Hetchy has limited hours, esp. in winter.
I've heard that the park will not go to self-registration permits on Oct. 15 like would normally happen, and instead will continue the online permit process indefinitely. In the past few years trailheads from Yosemite Valley required getting a permit in person at the valley visitors' center, and trailheads starting from Badger Pass (when open) require getting a permit a the "A" frame building at Badger Pass.
Lastly, as a reminder, there will be no overnight parking on the Tioga Road from Crane Flat to Tioga Pass, or along the Glacier Point road, starting Oct. 15, even though you can get permits for trailheads starting on the Tioga Road after that date.
