Check out this website for any information on open roads. https://goldentroutwilderness.wordpress.com/
I usually do at least one hike there each year (sometimes more) as the trailheads are closer to SoCal. By memorial weekend in May, you often can get access to some of the nicer parts (if it wasn’t a big snow year) and hike often into sometime in November. But many of the roads for the remote trailheads close for the season once the snow starts to fly in quantity.
There are a lot of nice meadows, a few high peaks, deep canyons, some hotsprings, but note that some of the trails are in poor condition. Most are still hikeable, but I do recommend carrying some sort of GPS device with the trails loaded. Cattle grazing is allowed in parts so the cows also complicate things by making their own trails that seem more distinct then the real ones.
Permits are easy to get. If you hike in from Blackrock, the permits are self issue. Coming in from the west, I’ve had permits left outside of the ranger station in Springville and picked them up at midnight as I drove through. Don’t recommend getting one from Lone Pine Ranger Station unless it isn’t a weekend. There is usually a big line and they often use lotteries to pick the order instead of first come first serve even though the trails into Golden Trout don’t have quotas; at least if you aren’t planning on hiking into Sequoia National Park the first day.
Here are some photos of a trip I did over July 4th weekend in 2017 that was a big loop through the eastern half (got the route from a recommended trip from the website I noted at the top). A nearby fire started just before I arrived and you can see the smoke in some of the photos. I have plenty of other photos from other trips in other parts, just don’t have them uploaded anywhere at the moment.