I've flown over New Year's Eve twice before, both on a YVR-AMS with KLM.
The first time there was an announcement when we passed over the timezone where it was midnight. The crew passed through the cabin and handed out champagne to those passengers who were awake.
The second time there was an announcement made at the beginning of the flight that there would be no announcement as we passed over the midnight line to avoid disturbing sleeping passenger but the crew passed through the cabin with champagne for those passengers who were awake.
Landing on New Year's Day was great as the airports were nice and quiet.