Even if you're used to skiing trips remember that Livgno is 1900mt, therefore it can be very, very cold, it's not unusual for the temperatures to reach -30 in December & January so take extra warm clothes.
Miscellaneous: Don't even think about buying dutyfree goods at the airport, you'll find them much cheaper in Livigno.
It can get pretty cold even in summer so get some long sleeved sweaters and a jacket, along with your summer clothes. It doesn't rain much in Livigno, however an umbrella may come in handy especially in July/August.
Toiletries and Medical Supplies: Most hotels in Livigno are 3 star hotels and they only provide toiletries for the first day of your stay.