If you're looking for a snow free hike, I'd look elsewhere, or wait a few weeks.
From my BC skiing travels over the last several weeks...
- Snow at and below Timberline Lodge.
- Mt Hood Meadows snow levels are 300-400' above the base area.
- Elk Cove on the north side has snow.
- Snow level on the Cooper Spur side is around the Tilly Jane Hut. The road to Copper Spur is supposed to open sometime mid July.
There are plenty of TH's that you can access the Timberline trail for a shorter snow free hike, but I don't think you'll be able to do the complete trail without post holing through knee deep snow for long stretches.
Check out "Portland Hikers" for good up to date beta on trail conditions.
I only ride bikes to fill the time when I'm not skiing.