There are several separate issues involved with your question. Let's look at each in turn.

Sudden temperature changes

When materials are subjected to sudden temperature changes they can tolerate the change or can be irreversibly damaged. It all depends on the materials involved, the temperature extremes involved, and just how rapid the change is. Take any lens element heated to something like 300-400°F and drop it into a bucket of ice water and it will most likely crack. That doesn't mean walking out of your 75°F house into 0°F winter will have the same effect. In fact, it almost certainly will not.

Although 0°F is a little extreme, moving from room temperature to outside where the temperature is just below freezing doesn't seem to permanently harm cameras and lenses. What it does do is affect the battery that powers the camera (more on that in a bit). When ideal optical performance is required in cold weather, such as for astrophotography, allowing all of the optical components to stabilize at the ambient temperature before starting to shoot will avoid temporary minor optical issues due to different parts of the lens/camera cooling at different rates.

Moving from warm to cold environments is usually a lot easier on camera gear, in terms of long term health, than the opposite. The primary culprit is humidity.

Humidity and condensation

Condensation and moisture can damage your camera and lenses in several ways.

• Moisture can affect the electronics, particularly if a circuit is powered while wet. Allowing voltage to be applied to a circuit board while it is wet is a recipe for disaster. It will very often fry the electronics instantly.
• Condensation can leave mineral deposits behind on optical surfaces when it dries. It can also "weld" dust to lens elements or the camera's sensor and filter stack immediately in front of the sensor.
• If moisture is combined with a warm and dark environment, it can result in fungus growing inside the lens or camera. Keep in mind that fungus spores spread via air and are everywhere. So is dust. Even brand new lenses have dust in them. Those brand new lenses also probably have fungus spores in them. It's a biological fact of life when present in the Earth's atmosphere.

The most common cause of condensation on camera gear is caused by moving a cold camera and/or lens into a warm, humid environment. If the temperature of the camera or lens is below the dew point of the surrounding air, water droplets will condense on the cooler surfaces. This should be avoided as much as possible.

The easiest way to avoid condensation is to always put the camera/lens into a sealed bag before moving it from a cold to warm environment. The cold air sealed into the bag will contain less moisture than the warm air inside buildings. Leave the bag closed until the contents have warmed to room temperature. Any condensation that forms will do so on the exterior of the bag.

Cold and Batteries

Batteries are chemical devices that depend on chemical reactions to supply electricity. Those chemical reactions are affected by temperature. When batteries get very cold, their voltage drops rapidly. A battery that will power your camera for hundreds of shots at room temperature might only manage a few dozen frames in sub-freezing weather. The good news is that just warming the battery up restores some of its energy. If shooting in cold weather, carry plenty of spare batteries. Keep them warm inside your clothing. Swap the batteries in your camera and the warm batteries inside your clothes often.

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