Can i take my digital camera into a freezing environment?

Hi I'm trekking to everest base camp, where temperatures can get well below freezing and wanted to know how my digital camera will function. I understand you can get freeze proof, underwater type cameras, but would a regular digital still function, does it just mean short battery life or would it not turn on at all.
Same question for my iPhone (not for calls, purely for the camera capability)

Condensation can be an issue when going from cold outside to warmer shelter. Ziplock bags help. You could keep spare batteries warm close to your body.

If you can keep the camera warm, then it will work fine in the freezing environment for the short period you take it out and use it.

The biggest problem is the battery. You can remove it and keep it against your body in a pouch - and it should stay warm. Also, if your camera uses AA batteries, buy Lithium non-rechargeable as they work at lower temperatures (down to -40C).

Some things I did in the course of taking this picture:

I kept handwarmer packs in my padded case to keep the camera warm in transport.
I had a clean cotton handkerchief in there to wipe off condensation.
I used two layers of glove liners with handwarmer packs to have enough dexterity to operate the camera without getting my fingers frostbitten. I kept my hands in my pockets a lot.
I used a tripod with a quick release plate. I mostly walked around with my open tripod tucked under my arm. I thought out the shot a lot before deploying the camera to minimize exposure.
I carried a spare battery in my pocket.
I brought a lot of handwarmer packs. I could have bought more at the supermarket if needed.

I don't know if it will come up on your Everest trip, but for pictures like this I had a toothbrush in my camera bag.

A toothbrush? It is to clean the snow off of the raised metal letters on the plaque to make them readable.

Mike, when the fog rolls in or it starts raining, its gonna get wet. If you go to an extreme environment, you will need a camera that can handle it. Fog, rain, snow, ice-rain.

No problem at all, I use my Canon 6d and Olympus XZ-2 everyday in temperatures as low as -25C here in Finland.
Sometimes there can be some condensation on lenses when you move between warm and cold places instantaneously, but that goes away by itself in a few minutes.

Everest? No. Use film.