Bit too early to tell, but based on past seasons and this seasons snow, there is a good chance you will have snow to hike in, particularly above Trail Camp. If you don't need traction climbing up, you might need traction descending especially if you are coming down late in the day as the sun will not be hitting the northern aspects of the route then. Places like the Cables area will likely have packed snow where crampons or some other traction will be helpful if not required for a safe trip down.
As far as an axe, again too early to say for sure, but it can't hurt to start getting practice in as you might need it as well in those same spots.
