In addition, extremely low temperatures are hard on batteries. Batteries do not produce as much charge at lower temperatures for starting, which is why they are rated in CCA, or Cold Cranking Amps.
I agree with Joe, replacing the alternator would probably be a good idea, and the alternator and battery should be replaced together. The reason is, a bad battery will overstress an alternator trying to charge it, which will blow the diodes out of the rectifier. Alternately, a blown rectifier will not properly charge a battery, and the battery will fail due to plate sulfation. Before I learned about this, I had an El Camino that had a bad battery. I was also broke at the time, and had to nurse it along. When I finally replaced the battery, I'd blown the alternator. When the battery failed shortly after, I assumed the alt was bad. Shortly after, the battery was dead again. Etcetera. After a few batteries and alternators, I decided to replace both at once and that broke the cycle.
As a side note, a buddy of my dad's worked for Exide Battery Corp as an engineer. He told my dad that they did battery testing, and found that if you put your car on a battery charger for an hour once a week that your battery would last forever. Too much trouble for me right now, but one day I might give it a try.
If your battery is bad enough to replace, replace the alternator and battery together.
I would also note that unless the trunk leaked enough water to damage the battery case when it froze via mechanical damage (water expands when it freezes, interesting that it also expands when it boils), that the trunk water leak would have nothing to do with the battery failing unless the water vapor caused corrosion around the battery terminals. The case is plastic, and therefore is waterproof.