I'll bet certain stretches of the trail are relatively free of snow, or at least well on their way. However, as that thread suggests, it is sure to be quite deep snow and slower going for an extended section above Lake Park, probably on the approach to Bison Peak and along the river gulch west of the TH as well. It all depends on what you are willing to slog through, I guess. There aren't really any technical sections, so the primary consequence of snow is that you have to hike in snow, or bring along some snowshoes.
Long as the TH is accessible, and you don't mind turning back if the conditions warrant or spending an extra night due to slow progress, could be worth a shot! Others might have better info than me.