Lens is stuck in the open position and when i try and turn on the camera, it makes a clicking sound and displays a LENS ERROR message

Sounds like the drive motor assembly has quit. this needs to be repaired by shop, probably had nothing to do with the cold.

Try the procedures in this tip.

Zoom error/ lens cover is stuck in open position

Hi,
    As in short answer you have to replace the optical lens assymbly.Because due to heavy jurk its motor called sledge motor stsrt malfunctioning and it can not be changed component level. For this please contact any SONY SERVICE CENTRE nearby to you.
Hope you will understand.
Thanks for using FIXYA!

try smacking the sides of camera.also try to make the lens up down with you hand couple of times.then check out.

Lens jams can happen without dropping the camera. The lens motor is bad, or a grain of sand has got stuck in one of the lens cogs. Either way will need lens repair/replacement.

My Camera: Canon PowerShot SD770 IS Digital Camera

Went to the beach yesterday, by the end of the night my camera gave me this error: "lens error, restart camera". The lens would no longer come out.

I figured sand got stuck within the lens, so I did the following:

1. Turn camera up-side-down (with lens facing down)
2. Gently tap the sides of the camera (to loosen particles in lens)
3. Turn camera on
4. The lens will eventually come out
5. Gently tap the sides of the lens
6. Turn camera off (continue tapping side of lens as it retracts)

I turned the camera on and off a couple of times to ensure I removed all sand particles from the camera.

Now the camera works...thank god.

This is probably THE most common failure among digital cameras. There's a halfway chance of fixing it yourself, described here: http://camerarepair.blogspot.com/2007/12/fixing-lens-error-on-digital-camera.html

try little rubbing alcohol around outer surface of lense this should loosen up the sticky ness of it
remove the memmory card and turn on this should reset camera

tuen on camera then press display a few times. it sounds like the display is just turned off. the lens system should be open.