In Into the Universe with Stephen Hawking, Hawking describes a form of nitrogen- and silicon-based life evolving on a frigid planet. Is this really viable, and would a similar biochemistry work on a planet with fields of methane snow?
I beg to differ: No
While all points raised by madscientist159 are fine, silicon based life hypothesis has a one, incredibly large, hole in it. That would be the amounts of energy required to cross the activation barrier in typical silicone reactions. One needs to pump A LOT more energy to force silicon to react, especially if you want to make silicon chains analogous to what carbon does.
If anything, I would expect the silicone based life to evolve on something as hot as venus (but not venus itself due to redox and ph issues).
Yes -- within limits
Assuming a planet sized to yield Earth-like atmospheric pressures, the first problem would be how close the melting point of methane (-182C at 1ATM) and the boiling point of nitrogen (-195 at 1ATM) are. You may not be able to have much in the way of guaranteed methane snow on the ground before you run into your working gas liquifying; conversely, if your lifeforms "breathe" liquid nitrogen they may not be able to venture out of the snowy areas. Plus, the snow would be on top of the liquid nitrogen similar to the Arctic regions on Earth.
If the surface of your planet is under significantly lower pressure (small moon?) the nitrogen would stay as a gas, and this also yields interesting possibilities with the lower gravity and smaller planet surface area that would be present.
Any lifeforms at these temperatures are probably not going to be the high energy forms of life we are familiar with here on comparably warm Earth. All metabolic processes would need to be slower due to the lower energies involved; this may retarding complexity of any organisms formed as well as the potential intelligence of smaller organisms. Even if complex life does form, the resultant intelligence may not be recognizable to species that operate on much shorter timescales such as humans.