If you want to wish your sister a happy new year and you are not there to hug her personally, maybe you should write her a letter in such a way that she feels like you are there. Since sisters are relatively more emotional, your letter should have all the emotional things which you have to say to her.
Start off by inquiring about her health and then simply wish her a happy New Year. Tell her how you miss her during this time of the year and would wish the two of you could be together. Your tone can be informal and casual since you are writing to a family member.
Sample of New Year Letter to Sister
Number 8 Public Lane,
Bloke House 23847
London, UK 3489
I hope this letter has found you in good health. I am writing to you to wish you a happy New Year. It has only been a week since I last wrote to you for Christmas and I have been missing you so much that I decided to write a letter to you again.
I received your reply for the Christmas letter and I must say that the card and pictures you sent me brought a few tears in my eyes. Not having you around during these holidays is something extremely hard and right now I am wishing that I could somehow fly to you all the way from New York just to spend a little time with you. However, sometimes in life you must go through some stern tests and I am going through it right now.
I have been praying a lot of you and I hope that you and your little kids, Joey and Beretta, are doing fine. I will be sending them gifts in February because I am running out of cash this month.
Lots of love for you and your family!