When cranking a good battery should not drop below 10volts, when started you should have 14-14.5Volts back at the battery.
Starting a cold car is alot harder then starting a warm car, so if your starter is worn - she will struggle. Also once the car has been running for a while the battery will store a surface charge, That will give the starter more amps to deliver when cranking - so if starts easier. The surface charge disappears after 1-2hrs