Car battery flat after cold/wet weather..?

Would anyone know why my battery is going flat or almost flat in the morning following cold and wet weather? i recently replaced the battery (2 weeks ago). the car was also fully serviced at this time. there is nothing that can be draining the battery overnight such as lights, etc. the car is fine when starting when it is not cold. could it be the alternator? what do you suggest i do or try? and prices to get it sorted ? it is a rover 214si, 1.4, 1999. cheers!
Answer
Take the car to a local tyre and battery depot and they probably check both the battery and the alternator plus give you a decent price for a replacement. the are doing it day after day.