Looking at the webcam view today, with no snow on Thor Peak at 12,300', the trail will be pretty much clear of snow to Trail Camp. But I am sure you will encounter some icy sections.
There just isn't enough snow, and especially hard-packed snow to use an ice axe. Microspikes and hiking poles would be better than crampons and ice axe, since there is lots of exposed rock on the trail.
Richard P hiked the trail Oct. 26, and took these pictures: