Can I use a digital camera (olympus FE370 ) to take pictures at temp. between - 6 deg and 10 deg C ?

In the cold batteries don't last so long and electronics, such as those used for focusing and metering loose some of their accuracy. While your camera will probably be fine in the cold, performance won't be 100%. It is unlikely to cause permanent damage though and battery operation should return to normal with the temperature. Keep the camera in a bag or ideally inside your clothing until you are ready to take pictures, then return it as soon as possible after wards. Once you're done taking pictures, return the camera to somewhere warm and dry to warm up. Nothing too hot and definitely nothing wet or damp. Leave the camera there to warm up slowly with the memory card and batteries removed and all the doors and flaps open. This prevents the build up of moisture or condensation in the insides of the camera.