Before you condemn the alternator - it could be your battery. Use this procedure to check it. Charge your battery. Let the car sit for 8 hours. Check the voltage on the battery without trying to start your car - it should be 12.56 volts MINIMUM - a real good battery will be about 12.72 or higher. If your voltage on the battery is 12.1 volts after 8 hours of rest - you have a shorted cell. If your battery reserve is too low because the battery is bad as determined from the above test - your alternator will not be able to keep up with the current draw of your car causing the low 11 volt reading because your battery does not have the reserve to keep it above 12.5 volts. Cold weather will make things worse with the battery. Good luck
Morris