some auto shops will sell you a battery, then next week sell you an alternator. high rate discharge testers dont locate build ups between the plates or self discharge, the age of the battery tell alot.
A cold snap will show up loss of performance in a battery esp if its on its last legs, it could have started the vehicle all year the one cold day, click click click.
its worth renewing your batter (diy) as a matter of course as its often far cheeper, check boot lights first. The the alternator works better in cold but the the battery dies.
try...
Charge batter to full state via external charger vehicle now starts with ease, now turn head lights on for 10 mins (approx) with enging off. If car fails to now start or wow wow wow click..renew battery, its going to let you down anyway.
A good battery voltage should be around 12.6v off load after around 3 hours of none use and 13.6v to around 13.8v after the alternator has cut in just after idle speed (give it a rev) you can hear the alternator sing when it cuts in if you know what your listening for.
hope this helps