I spent 10 days in Rome in February of this year. I was lucky with the weather, with the daily high temperatures getting well into the 50s F. However, be aware that it can be in the 30s until very late in the morning or even noon, so you'll start out early each day wearing layers and then (if you're lucky) disrobe as the day goes on.
Some cafes in smaller museums were not operating, but I don't know whether that was a typical seasonal situation or the lingering effects of COVID. I observed no problems with sights themselves, but it's common to find separate schedules for winter and summer, so you should check operating hours on line in December to be sure you're working with current information.
Pre-book anymore these attractions you want to see: Colosseum, Vatican Museums, Borghese Gallery, Domus Aurea. Tickets for San Clemente cannot be purchased at the church, but you can get them online just a day or two ahead, unless something has changed recently.
Restaurants and cafes were up and running. You'll have no issue there.
I have a relatively comprehensive sightseeing list I put together for my trip that I'll be glad to share, but I'm in Europe right now and won't return home till sometime in October. If you send me a private message on this forum in late October, giving me your email address, I'll be happy to send my notes to you if you think they'll help.
If you like Art Nouveau architecture, I highly recommend the Quartiere Coppede.