Sorry I do not know as I stayed mid December. You could email the hotel as they were very helpful during my stay.
Guess it's a little late for this year, but yes the hotel had a New Year's Eve party. More specifically, the rooftop restaurant, The Gutenbergs Terase (with a great view of the Riga Cathedral), had a New Year's Eve party.
Get an answer from Hotel Gutenbergs staff and past guests.