All batteries deliver their power via a chemical reaction inside the battery that releases electrons.
When the temperature drops the chemical reactions happen more slowly and the battery cannot produce the same current that it can at room temperature. A change of ten degrees can sap 50% of a battery's output.
In some situations the chemical reactions will happen so slowly and give so little power that the battery will appear to be dead when in fact if it is warmed up it will go right back to normal output.
Photo shows a Chevy Volt charging.
Now, if the cars were cheaper than gas-powered cars of equal performance, these cold-weather risks might be acceptable. But electrics are substantially more expensive than cars of greater capability - and will be for years to come.
Why is it that 'greenies' continue to push one of the least green technologies available. The materials that make up the battery are toxic, the methods used to mine them are toxic, crashes will release spills that create environmental issues, and recycling the material will create vast new waste streams that can kill water sources.
My personal experience with electric vehicles? Several years ago I drove one nearly every weekend during the summer months and it got me from the 1st tee to the 18th green nearly every time without recharging.
There is a report at the second link below detailing a trip in an electric Mini Cooper from London to Edinburgh that took longer than a stagecoach did in the 1830's!
Link here and here.