Here is how Titleist Customer Service would answer the question of cold weather effects on golf balls.
Golf balls are designed to work best at temperatures around 70°F. If they get a lot colder than that, the feel will become harder, there will be a moderate loss of distance, and the greenside responsiveness will decline. Much hotter than that, and durability may suffer, there may be excessive spin, and any distance gain will be minimal or nonexistent. Thus, we recommend storing golf balls indoors at room temperature between rounds, so that they remain near 70°.
Thank you for your question regarding Titleist golf balls. While we do not have specific data available to be shared, there are really two aspects to the question of temperature: the temperature of the ball itself, and the temperature of the air it's flying through. When the ball gets cold, the materials lose some resilience ("bounciness") so they come off the clubface slower and thus lose some distance. The materials also firm up, which makes the ball feel harder on impact. Since most golf balls these days use similar materials inside, these effects will also tend to be similar. Of course, these factors can be easily minimized or eliminated by not letting the ball get cold. We always recommend that golf balls be stored indoors at room temperature between rounds, and that's especially important during cold or hot times. If it's really cold outside, it's not a bad idea to alternate two balls hole-by-hole, keeping the idle one in a warm pocket.
The air temperature affects ball flight because colder air is denser ("heavier") and thus caused greater aerodynamic drag. There is nothing you can do about this one, and it will affect different types of balls in essentially the same way. It's not a huge effect but it can be significant. The distance loss between a 70° day and a 40° day, for example, will be somewhere in the ballpark of 2%.