You can tell a cold morning by the high-pitched crackle of ice under your feet. Have you ever broken a tool while working on your car outside in the winter? Or dropped a plastic lunch container out of the freezer and seen the corner break off? Cold and brittleness are inextricably linked in people's minds, but on the surface there's no real reason for it. I'll put on my lab coat for a moment here and go a little deeper.
Steel is the classic example. There was speculation that the Titanic sank because the iron hull had been embrittled by the frigid waters of the north Atlantic. It's true that during World War II, twelve Liberty-class cargo ships broke in half. The ensuing research uncovered the cause: the ductile-to-brittle transition in bcc metals. Steel is an example of a bcc metal (which refers to the arrangement of the atoms in the structure) and when warm it can be bent quite a bit before it breaks (it is ductile). However, at around the temperature of ice water, the tiny crystals that make up steel parts harden to the point where cracks simply separate them, instead of the crystals stretching to blunt the tip of the advancing crack. These free-running cracks then allow the part to simply break in two.
Those tiny crystals (above) are at the root of most of this behavior. As I mentioned, the atoms in each crystal are arranged in an orderly fashion, which allows them to deform in a similarly orderly fashion. Now, the amount of force it takes to deform a crystal is smaller at high temperatures. (That's why the World Trade Center buildings didn't collapse immediately when they were hit by planes: it only happened after the jet fuel fire softened and bent the steel girders.) But the amount of force needed to pry two neighboring crystals apart doesn't change. That means that when it gets cold enough, steel cracks like styrofoam instead of each crystal pulling like taffy.
What about the lunch containers that crack when they fall out of the freezer? They're not metal. It turns out that plastics have a "glass transition temperature" above which they are softer. Window glass has such a temperature too, but it's red hot; the same word is used because plastics and glasses both have a random atomic arrangement. Above the glass transition temperature, plastics and glasses respond quickly to external forces - picture a glassblower bending red hot glass. So when you drop a cold plastic tub, it can't change shape fast enough to deal with the impact and it breaks.
So maybe there's something behind the perception that everything gets brittle in the cold. Everything I've talked about here is based on the mobility of atoms, which vibrate more at higher temperatures. Those vibrations allow plastics to flow and metals to deform. And there's your materials science lesson for the day!