Massive pangs of nostalgia over here.
When I was a kid, my folks would take us to Italy for Christmas every few years. You're in for a treat... no crowds, Piazza Navona, roasting chestnuts on every corner, and for a Catholic family, being at the Vatican for Christmas is pretty special. It's still my favorite time of year to go, though I haven't been for the holidays in over a decade, so maybe everything's different now.
You'll definitely have to contend with things being closed. As I remember, Christmas day was the only day that was really difficult. The surrounding days, though many restaurants were closed (ditto museums and attractions), there was always a corner trattoria somewhere to fall into. It's been a while, but while the time of year will limit your options, perhaps substantially, I don't think you'll have a problem finding places to eat. Of course, as mentioned, this is all fuzzy kid memory, rather outdated, and may no longer apply. If anything, I expect more will be open nowadays, as Italian business hours only seem to be expanding. But even if it's how I remember, I'm of the opinion that it's a perfectly acceptable trade off. There's something really special about Rome at Christmastime.
Dominic Armato
Dining Critic
The Arizona Republic and
azcentral.com