Thought that was a Crosby, Stills, Nash, and Young song.?
Nope. But they did do a good cover of it.
Ironically, Joni never made it to Woodstock. Her agent told her the traffic situation was a nightmare and so she better stay in the city (NYC) so as not to miss her chance at being on the Dick Cavett show. YouTube "Dick Cavett Woodstock show" and you'll see Joni, along with Stephen Stills, David Crosby, and Jefferson Airplane members sitting around being interviewed by Dick Cavett. Stills, Crosby, and the Airplane had just finished playing Woodstock. Joni was reportedly a little pissed at her agent for quite some time.
But she did write the song.