I did this hike last weekend. The previous weekend I was in a different area of this park, and had no snow/ice the whole trip.
I brought my microspikes with me, which seemed like overkill (given there was no snow on the ground), but I had remembered hiking here before & had a recollection that the trail was narrow and could be icy. I'm very glad I brought them. Even though there was no snow, the Stillman Trail had some bad ice flows. I met some hikers who had no microspikes and they found it very difficult and had to hike off trail. I did bring microspikes, but they were not even adequate in some areas with very hard ice (they weren't biting into the ice adequately).
Some photos showing the ice across the trail: