Recent article published by PLOS ONE claimed that Open Access has a significant share in the field of Arts and Humanities. In fact, according to this study, humanities are approximately as open as biology, chemistry or mathematics.
The most open fields are computer science, followed by geosciences and physics.
Observational errors might be quite high, so I will not cite exact numbers.
More good news: there is about 120 million scholarly articles on the web and a quarter of them are available for free. Even though you cannot read them all in your lifetime, your computer can probably mine them all.