If it turns over but wont start until you jump it then it may well be a voltage related problem. All the computers and electronics are really finicky in newer cars. The reduced power coming from a colder battery may be messing with the ECU in some way, although there would have to be some other underlying problem.
I don't know if BMWs are different, but every car I know of that has a computer chip in the key doesn't prevent the fuel pump from turning on. It will turn off the car after like 5 seconds after you start it, otherwise the delay for time it takes the computer to try to recognize the key when you try to start the car would be really annoying.
Also if the engine is turning over and not starting it is really unlikely to be a bad starter. Especially as everyone else is saying that the fuel pump isn't turning on.