When I first saw the title of this thread, I thought it was about a water additive for firefighting ( http://www.firefreeze.com/ )
Regardless, we’ve been through this before (with all due regards to stuyguy), and I’ll try to work through it again.
First, some very basic fire science stuff (I taught this to three 5th grade classes last week). We’ve all been taught about the Fire Triangle, you need fuel, heat, and oxygen for a fire to start. The one that the public isn’t taught about (but we teach in the fire service) is the Fire Tetrahedron: fuel, heat, oxygen, and an uninhbited chemical chain reaction. Too little of any one of these four, and the fire goes out. A balance is needed between the four elements. Also, you can start a fire with the Triangle, but you need the Tetrahedron to sustain it.
With that in mind, lets look at a fire (this is very generalized…I don’t have the energy to go into the minute details).
We have a small fire at the end of the cigarette. When we start it, we have the fuel (the cig.), the oxygen (ambient in the air) and the heat (first from the match/lighter, then generated from the fire itself). Once sustained burning begins, toss in the uninhibited chemical chain reaction that keeps it going.
Now, take this small fire at the end of the cigarette and move it into a cold (but tolerable by the smoker) enviroment. The cigarette is still going to produce enough heat to maintain that chemical chain reation. More heat is going to be lost to the enviroment through radiation and convection (not too much by conduction) since the air around the fire is colder, but its not going to be significant.
Now, instead of the cigarette being in a human-tolerable cold enviroment, put it in an ungodly cold enviroment. We’re talking -300 F here (thats a complete WAG, but you get the idea of freakin’ cold). Get down that low, the fire will lose so much heat to the enviroment that it no longer has enough heat* to feed back into itself and allow combustion continue.
I don’t have numbers to tell exactly what temperature that fire is going to go out at. Its going to depend on the rate of heat release of the fuel, available oxygen, air currents around the material, distance to nearby objects, and of course the ambient temperatre, amongst other things. But, cool down the enviroment around the fire enough, and the fire will go out.
While I’m here…
Surgoshan, there are 4 ways to put out a fire: remove the heat, remove the oxygen, remove the fuel, or interrupt the chemical chain reaction. Water removes the heat, CO2 removes the oxygen, removing the fuel is used in forest fires (firebreaks), dry chemical and halons interrupt the chain reaction. Pretty easy, huh? 
- The heat from the fire heats up the fuel, pyrolizing the material into combustible vapors. If the fire can’t produce enough heat to continue pyrolosys (that spelling looks wrong, but I’m too tired to look it up), the fire’s going to go out.