Cold weather will always find a duff cell in a battery, especially if it drops below zero. For each degree below "normal", the output (capacity to deliver) drops accordingly also.

Thats true, some Fords now have very special charging systems.

Bloomin heck, the original in my Ford lasted 9 years and it's replacement is fine at 5 years, bought in panic from a factor. We thought the one in the Astra was knackered but it's fine in the Corsa, 12 years old. I think I overcharged the original Corsa battery but it still works at 10 years, the little thing started up the big nasty diesel ok last week.

What I think I'm trying to say is, generally, batteries will last ages, given a good charging system. If your charging system consistently leaves the battery under-charged, the battery will last less time. If it overcharges, it may fry a battery within a year.

Probably the alternator. But don't just replace it without working out, exactly, that the alternator is at fault. No good throwing money at it, you need to check everything that could lead to a drain on the battery, carefully and methodically.