In a car without four-wheel drive—if the car provides drive power on only two wheels—why put snow tires on all four wheels when the freeze sets in? Would it not be sufficient to change just the drive wheels? Is it just a question of use of the wheels and the extra use of two wheels for 12 months, while the other two pairs are being used nine months and three months would complicate things like wheel rotation?
Related: need for matching tires on 4-wheel drive cars
About braking: In this question we're more concerned about avoiding to get stuck. It's reasonably clear that having four winter tires offers better braking, but we are in this instant comparing four non-winter tires with two winter and two non-winter. Regardless, after you read Paulster's answer, it will be easy to extrapolate what would happen if your car was not oriented in the direction of motion and you attempted to brake, but someone who brakes during turns over snow or ice, with any kind of tires, is probably in a very bad position anyway.
Context (edit #2, after Harper's answer)
I am asking this question after giving up on moving from a parking lot, which required going up the mildest slope. After many, many, attempts I abandonned the car and used cabs for the day. Since I wasn't sure whether I could be towed from the rear of the car, I asked the question with the objective of buying two winter tires and installing them on the front wheels (on a FWD car).
Curious phenomenon, by the way: if the wheels spin out (as they must if you're stuck), and if the temperature and snow underneath are in just the "right" conditions, the mere heat generated by a little bit of spinning (it's manual-drive and I was careful) will melt the snow and form a nice layer of pure, ultra-slick ice in very little time. But now we're way out of car mechanics and into the physics of water.
In the evening the ice was less hard. Or maybe I managed to get out after pouring an obscene amount of salt, which may have acted as a gravel carpet more so than a melting point modifier.