In reply to GeorgeR:
My wife and I walked up Teide last February on dry paths apart from one or two icy steps near the top. I don't know how typical that was, but there was very little white near the top, and the whole thing is on a well made and obvious path.
We set off at midnight and walked easily to the summit ready for sunrise. There is a gated summit path away from the cable car. You don't require a permit if you pass the gate and get up to the summit before sunrise, and then leave immediately afterward. The hut near the summit looked well organised, and I'd probably go for that along with the permit if I was organised enough to book in advance!
A really worthwhile outing. We then walked out via another volcanic summit to the Parador hotel before getting a bus back to our car, which made for a nice itinerary.
Enjoy it.
Hams