Look out for Sunday-esque frequencies during the night. Also, as the 1st is a Sunday, the trains are gonna stop running at 0430 until ~0630-0700, 0600 earliest.
That's not true. Services will operate throughout the night and their frequencies will be lower than any normal Sunday.
In fact there are lower service frequencies throughout Saturday 31st Dec/Sunday 1st January. I only have the Met timetable to hand but it might give you an idea what to expect on other lines.
The Met is operating as follows:
Start of traffic 31st December: normal Saturday times.
Start to 07:00/0730 (Sat)
Uxbridge to Aldgate every 15 minutes
Watford to Baker Street every 30 minutes
Amersham to Aldgate every 40 minutes
Chesham to Aldgate every 40 minutes
07:00/07:30 (Sat) to 04:00 (Sun)
Uxbridge to Aldgate every 20 minutes (normally every 15)
Uxbridge to Baker Street every 20 minutes (normally every 15)
Watford to Baker Street every 20 minutes (normally every 15)
Amersham to Aldgate every 40 minutes (normally every 30)
Chesham to Aldgate every 40 minutes (normally every 30)
04:00 (Sun) to 10:00 (Sun)
Amersham to Baker Street via Watford every 60 minutes
Chesham to Baker Street via Watford every 60 minutes
Uxbridge to Baker Street every 30 minutes.
10:00 (Sun) to Close
Uxbridge to Aldgate every 20 minutes (normally every 15)
Uxbridge to Baker Street every 20 minutes (normally every 15)
Watford to Baker Street every 20 minutes (normally every 15)
Amersham to Aldgate every 40 minutes (normally every 30)
Chesham to Aldgate every 40 minutes (normally every 30)
Close of traffic normal Sunday times.