Cambridge dictionary suggests that "New Year" is the same as "new year". but the following examples suggests that they have different meaning:
The building work will happen in the new year.
But The Guardian usually use at instead of in
Sifting through contradictory evidence is common when it comes to choosing the right thing to do to improve our health, not least at new year when many of us promise to leave old habits behind and make a fresh start. See the source here
What is the difference in meaning?