1993 Toyota Camry hard starts and rough idle in wet weather

Hi there, after it rains or when it is wet outside my car has trouble starting right away. When it does end up starting it sputters and and runs very rough and shakes the whole car. Even if I apply the gas it still sputters terribly. I also notice if I turn on any accessories it only seems to make the problem even worse. It only remains this way however for a minute or two until the engine warms up and then it runs fine. I just had the alternator checked and the battery replaced by a mechanic a week ago, so I was wondering what your thoughts were on the situation? Thanks so much!