According to
Cesare Ripa, Iconologia 1593 edition:
Le due Faccie significano che la Prudenza è una cagnitione vera
et certa, la quale ordina ciò che si deve fare et nasce dalla consideratio-
ne delle cose passate et delle future insieme.
...
Lo Specchiarsi significa la cognitione di se medesimo, non potendo
alcuno regolare le sue attioni, se i proprii difetti non conosce.
The two Faces mean that Prudence is true and certain knowledge. It decides what must be done and is generated by the consideration of past and future things at the same time.
...
The Mirror means the knowledge of oneself, since it is impossible to properly rule your action if you do not know your own defects.
One of the two faces looks behind, at the past, the other looks forward, at the future.
A prudence with three faces (including taking the present into account) can also be seen. Like in
this painting by Tiziano.
About the Snake, see the Gospel of Matthew:
010:016 Behold, I send you forth as sheep in the midst of wolves: be
ye therefore wise as serpents, and harmless as doves.
"Estote prudentes sicut Serpentes." (This reference also from the Bivio site).
Marco