Half way to Lone Pine lake, the trail disappears for 0.3 mile and you need to take one of the snow paths. Switchbacks are passable and pretty safe until the last stretch before Trail Crest. The easiest way is to climb up and bypass this part. Trail Crest to Summit, mostly dry, almost entire trail is safe and passable without crampoons, but there are two very short streches which are narrow and icy, so extra caution needed.
I camped one night at Trail Camp. It was quite cold(6-10F on my temp sensor at night), but no wind and no other people, so I really enjoyed it. I couldn't find any info about conditions, so I was prepared to camp up to 2 nights. It's possible to do a day hike, if you start early enough.
You can drive up and park by the closed gate around 1.5 mile from the trailhead. It's possible to do a day hike, but only, if you really know the trail and area and you're well prepared. Some parts of the trail and winter route could be very dangerous at night.