Having been a professional musician since the age of 16 (and it goes back before that in other forms) I can say that musicians (and I'm generalizing here) that use drugs are most likely self-medicating.
Also, just because Woody didn't have a coke-freakout on stage doesn't mean he wasn't using and/or using heavily. Drugs affect different people differently.
Many musicians are, in general, highly unstable people. Most have "chemical imbalances", bipolar disorders, self-worth issues, problems with depression, etc. etc. It goes with the territory. A lot of them choose to help these problems by self-medicating.
It's always fascinated me to find out how many of these problems (and they aren't just exclusive to musicians, obviously) are genetic and how many are the result of our society's lack of support for the truly gifted and creative.