And now for the rest of the story! Or the other side of the coin, as it maybe be.
In cold weather when you are wearing heavier clothing allowing for easier concealment of a larger, more powerful weapon, an attacker likewise would be wearing heavy clothing. Thus making a larger, more powerful round from a bigger gun much more likely to stop an attack than a mouse gun in 32, or 380 that can dissapear in your pocket wearing lighter clothing. The less powerful rounds being more likely at least adequate when the attacker is also dressed in much lighted cloths in hot weather.
Not to say that bigger isn't better in any weather, but having something is always better than having nothing. As mentioned in other posts, sometimes concealment is the number one concern.
Cheapshooter's rules of gun ownership #1: NEVER SELL OR TRADE ANYTHING!