You can answer it in a couple of ways:
* Formal: "El Año Nuevo es el primero de enero" (New Year's Day is January 1st)
* Informal: "El Año Nuevo es el 1 de enero" (New Year's Day is January 1st)
Both options are correct and will be understood. You can also add the year to the answer:
* "El Año Nuevo es el primero de enero del 2024" (New Year's Day is January 1st, 2024)