Woody was a pacifist, not just in belief, but in practice. Not only did he never use nor threaten physical violence; he also eschewed violence of thought and word. He would not verbally attack anyone, either in or out of their presence.
Woody went further than people normally go in applying the principals of nonviolence. He thought carefully about the consequences of his actions and labored to live a life that did not even indirectly result in violence. For example Woody protested policies of the U.S. government that resulted in the torture and death of innocents; minimized his use of resources whose extraction involves violence and injustice, such as petroleum; and avoided buying products whose manufacture involves inhumane labor practices.
Woody extended his principals of non-violence beyond humans. He was a vegan so that he would not contribute to the killing or slavery of animals. He avoided buying leather products for the same reason. He did not carry these principals to the extreme of, say, refusing to swat a mosquito. But he would not unnecessarily kill any animal. He literally would not hurt a fly.