Does DC-powered polarizing film exist?
While you can polarize an LCD screen with a DC voltage, if you do not switch polarity of the drive rapidly, you will plate the surface.  This kills the LCD.  So a polarizing film would normally have to be driven with an AC signal, typically a square wave.  

This could be as easy as using DC to power a fixed oscillator.  For a normal LCD.

You might want to look at a Boogie Board.  This is a physically changeable LCD with a click reset of crystal.  It is essentially a single LCD pixel.  That company makes an LCD bi-stable display.  It is similar to e-ink, but with LCD technology.  We visited the factor for these in Shenzhen late last year.  They can change pixels then let the hold.  While I don't know if this is DC driven, it is the closes thing to what you are looking for that I have seen.