Well, the purists ain't gonna like this, but and absolute "No it was not a folk festival" is a little strong.
If you remember back then there was a GREAT "folk movement" afoot that the more traditional folk people did not regard as folk in any way, shape or form. Example: Many of the popular (at that time) trio's were considered too commercial to be called folk. But that's all been hashed over before in the Cat, so I ain't said nothin' new.
BUT - a lot of people that liked the expanded notion of folk showed up at Woodstock, and to them it was folk. I don't want to take the time and bandwidth to argue this next point, but there is strong evidence to support the notion that folk music today would not be as popular as it is without the support of the non-purists. So maybe it wasn't truly folk, but it sure helped to popularize all of folk-type music.
Then there's another thing: If you were there and can remember what happened, you're not enough of a true folkie to judge what it was. If you're like the rest of us, and can remember driving in and some time later being on the road home, you have experienced the true sprite of Woodstock.
PS. BTW, did you know that if you type in 'folkie' and check it with spell checker, it suggests the proper spelling is 'phallic.' Now, Spaw, there's one fer you to elaborate on!!