Hi Helene,
My son and I did the LPL hike in mid November two years ago....ostensibly to go fishing. There were a few patches of snow on the trail. When we got to the lake, it had about 6 inches of ice already. So it was great for slip sliding around.
I loved the hike. It had a great late fall feel atmosphere. Nice and cool, but not cold. Of course, one storm can change all of that.