Good morning Harsh108
Nice that you are coming to Switzerland over Christmas and New Year.
The 3-day Swiss Pass is certainly a good option. The validity period for the activated days starts at 12:00 a.m. on the day of validity and ends at 5:00 a.m. on the following day.
Be aware that most of the touristic trains (Pilatus, Kleine Scheidegg-Jungfraujoch etc.) are not included in the Swiss Pass, but you have a discount of 50%.
Since you are traveling to Milan on January 1st, you will need an international ticket for that day from Interlaken or Lucerne to Milan. Therefore, a 4th day of the Pass is not necessary.
Do you have any further questions ? Write us. I am glad to help.
I already wish you a magical winter holiday in Switzerland. AntoinetteS