I've noticed my LCD going dim at cold temps as well. Usually it starts in the low-teens F. They just don't like the cold. Unless the battery is marginal, it doesn't effect the computer's operation. If the battery is old, as others have said, you could have issues.
I haven't had anything strange happen to my MTB or roadie since it started getting really cold.
I do not want to know what you do if your face gets cold during a ride...