Buying train tickets for late Dec and itinerary for first trip to Italy?

I bought tickets for Dec 16 adn 30 a few days ago. I just randomly pulled up Roma to Firenze for Dec 19 and the list populated with a full schedule of Freccia trains.

I would, with 13 nights, do Roma, Venezia and Firenze. I would weight the number of days somewhat on where you will be for Dec 25 as that will mostly be a "walking around" day, but Venezia is great for just that if that is where in your itinerary the holiday falls. Christmas Eve is pretty much business-as-usual although some sights willclose early. DO make reservations for 24th dinner and 25th lunch. It gets very busy in restaurants!

Giving us actual dates of the trip will help. Schedules for the high speed trains will come out first. I'd expect you will see them showing up on the schedule in mid October.
I will say that the Christmas Market in Verona is outstanding and leaves nothing to be desired from Suedtirol, Austria, and Germany. Yes, even Italians like a bratwurst smothered in sauerkraut on a bun with a cold draft beer. Very fun and a somewhat intermediate stop between Florence and Venice. Definitely spend 3 days in Venice.

Think of nights rather than days - a night is always a night, length of sightseeing time during a day can be shortened by travel, holidays, etc. I would add Benezia if at all possible. I lived in Roma on and off for several years and still find new things to do there, no matter how long you stay you will not see it all. Still, more is better than less.

In 12 days, you can definitely see all three cities. Exactly how many days to apportion to each one can be endlessly debated, and also depends on your interests.

As for train tickets, remember that if you can't book because the schedule has not been released, neither can anyone else. Just keep checking every day or two.

The schedule is out for many trains, but not quite all. Check and recheck every day until you find what you want.

Thanks so much for your very helpful replies!

I will be arriving in Italy the afternoon of December 18 and leaving in the afternoon of December 31st. I am 90% sure I will go to Venice for 3 nights (probably Dec. 23-26 or Dec 23-Dec 27). Am I missing out on a lot by spending Christmas Eve/Day in Venice rather than Rome? I will also look into the possibility of stopping in Verona for a few hours between Venice and Florence.

I would split my time ...
Rome - 4 nights
Venice - 3 nights
Florence - 6 nights
From Florence you have so many options for day excursions - Lucca, Pisa, Siena, Arezzo, Ravenna, Bologna.
I think Freccia train bookings are 120 days ahead, perhaps less around the timetable change.
I had no trouble bringing up possibilities to December 29.
http://www.trenitalia.com/tcom-en

EDIT Reading your dates now, and no, I wouldn't travel on Christmas Day. Padova is a good day option from Venice too.

You might want to hit Verona before Christmas as it has an excellent "Nuremberg Style" Christmas Market. Dates are not out yet, but it usually goes from 2 weeks before Christmas until the Sunday after Christmas.
http://www.christmasmarkets.com/Italy/verona-christmas-market.html

Spend more nights in Florence, as another poster suggested above, because Florence is the city from where you can take the most interesting day trips: Siena, Pisa, Cinque Terre, Chianti.
I would select a Siena day trip (not only the city is beautiful, but they produce delicious Christmas pastries) and a Pisa day trip (to see the leaning tower). I wouldn't do both in the same day, although some agency sells them together. I would instead add a Chianti region trip to your Siena trip, to enjoy some wine tasting in the place where it is produced.
About Cinque Terre: beautiful sea landscape, but considering the period of the year, I would reserve that for the next time, or eventually plan to do this last minute only if weather allows.
Here you can find a nice list of day trips from Florence: http://yourcontactinflorence.com/day-trips-from-florence/