I was up to Cottonwood Pass yesterday. The trail is virtually snow free right up to the Pass. There are some patches here and there but nothing dramatic that needs traction.
However, today I was going to do Cirque Peak from Cottonwood Lakes-South Fork lakes trail. While the trail from Cottonwood Lakes is clear to the 3.3 mile trail junction, there is quite a lot of snow once you turn off on the branch off to South Fork lakes. I think you could get there fine in the morning because the snow is firm but if you're returning in the afternoon you will post hole pretty deep as some of the snow banks were 3-5ft easy. I did not turn right up to Cottonwood Lakes (to new army pass) but at least from what I saw there was no snow on the initial portion of that section near the junction.
I also saw several sets of bear tracks on both trails, including a big print at 11,000 feet just before Cottonwood Pass. So, assume that bears are active in the area.