Extreme cold is exactly what makes BIC lighters a non-primary source of emergency fire.
As for the strips of inner tubes, a simpler method is to just get a big package of rubber bands from an office supply store. Wrap them around something in your kit and you have tinder.
And from a guy who was an Air Force survival instructor, a SAR consultant and went on to start his own company teaching survival (40+ years experience), the only truly waterproof matches are the ones sold by REI.