Ciao, Amanda,
Italy can be cold and dismal in January but it can also be clear and magical. If you want to avoid the crowds and have the place to yourself, then I say "come on down." You will be trading crowded outdoor restaurants for cozy, fireside osterie and trattorie. And that's not all bad. You will have Florence and Venice to yourself and parts of Rome, to boot. If I had to decide between the two, I would choose January, hands down.

"Did" Italy in February and November of last year (child away at school there) We would do it again in a minute. Most days were endurable, some were gifts of crystal clarity. I wore bulky sweater, decent wool gloves (bought superb leather ones there) and pants. Had a ball and noticed few closed venues. Lots of student groups though,so be patient.

I'm with the previous posters -- I'd go with January. I'm going at Christmas so have been doing some research on opening hours of museums. January 1 and 6 are holidays, but even then not everything is closed. Otherwise, things don't close down for the winter, though some may have shorter hours. Also, churches (open year round during mornings and late afternoon-early eves, with a midday closure), other than the well-lit biggies like St. Peter's, will likely be pretty dark in the late afternoon, so catch them in the morning when the light is better.

I'm planning to go to Rome in January & am looking forward to it. After speaking to a buddy who'd gone in January & said crowds were practically nil everywhere & getting too much sun or heat was never an issue, I figured it has to be worth a try!

BC

Also going in January. Couldn't resist
the price for the airline ticket and loved the cheaper hotel rates. I'll
miss the outdoor cafes but not the crowds! Have been checking closing times and most tourist sights close about an hour earlier in the winter. Just means we need to be up at the crack of dawn. Hope you have a wonderful trip!

Understand that Italy can be cold in January, but what about rain? Does it rain often in January?