Is it possible predict the oxidizing/reducing nature of a compound?
You may or may not be familiar with the concepts of electronegativity and oxidation states, but ultimately here is the rule of thumb you seek. If your compound contains highly electronegative elements not in their most negative oxidation state, expect it to be an oxidizer. If it contains elements with low electronegativity which are not in their most positive oxidation state, expect it to manifest at least some reducing properties.

On top of that, just like you anticipated, there is a whole lot of exceptions and subtleties which together constitute the magnificent field of elementary inorganic chemistry.